Ronaldo De

Carvalho Augusto

Aki Minoda

Oliver Rey

Céline Cosseau

Cristian Chaparro

Jeremie Vidal-Dupiol

Jean-François Allienne

David Duval

Silvain Pinaud

Sina Tönges

Ronaldo De Carvalho

Jérémie Vidal-Dupiol

Ranja Andriantsoa

Emilien Luquet

Fabien Aubret

Dia Sow

Patrice David

Vicki Thomson

Déborah Federico

Dominique Joly

Mariana Gomes Lima

Etienne Danchin

Christoph Grunau
email: christoph.grunau@univ-perp.fr

Chromatin structure changes in Daphnia populations upon exposure to environmental cues -or -The discovery of Wolterecks "Matrix"

Keywords: Epigenetics, ATAC-Seq, Daphnia pulex, norm of reaction, population epigenetics !

scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

1 1

Introduction

We are exploring here a classical battlefield of evolutionary biology. In a now landmark presentation in 1909, at the annual meeting of the German zoological society in Frankfurt, and at a time when oral presentations were still the major avenue for scientific exchange, "Mr. R. Woltereck (Leipzig)" exposed his ideas on Artveränderungen (change of species). The very same year, the scientific community had been captured by the publication of the German version of university lecture materials by the Danish botanist W. Johannsen, going back to 1903(Johannsen 1909). Johannsen had introduced the terms of phenotype and genotype to separate the outer impressions we have of an organism from the heritable components it has inside. He also had introduced the notion of "pure lines" on which selection would be powerless since offspring of selected phenotypes would still produce the same range of phenotypes. His work was based on the mutation theory of de Vries [START_REF] Vries | Species and varieties, their origin by mutation; lectures delivered at the University of California[END_REF] who had stated that the characters of organisms are made of distinct units that change spontaneously, salutatory, and relatively rarely. de Vries had called these changes Mutations. Mutations were in his eyes heritable and could be selected for. Woltereck's criticism was that the environment had nno influence on de Vries "mutations" or the "exact science of heritability" of Johannsen. This was counterintuitive to Woltereck and many fellow scientists who saw that the environment definitely had an impact on the phenotype. His battle horse became daphnia, easy to handle and cheap to maintain (contemporaries will understand the attractiveness of the system). Woltereck reasoned that, in response to Johannsen, further "analytical" experiments should also be done with "pure lines" (clonal lineages in modern terms), and with quantitative characters to investigate the role of the "milieu" (environment) on the character [START_REF] Woltereck | Weitere experimentelle Unter-suchungen uber Artveranderung, speziell uber das Wesen quantitativer Artunterschiede bei Daphniden[END_REF]). Woltereck recorded morphological measures, in particular the relative head length of his daphnia lines, depending on environmental conditions such as temperature and nutrition. These early studies paved the way to a subsequent rich literature that has documented the amazing property of daphnia to modify their phenotypes at the morphological, physiological, behavioral and more recently at the molecular levels in response to a large panel of environmental stressors including diet, pollution, heavy metals, and predator kairomones (reviewed in (Riessen 2011[START_REF] Harris | Daphnia as an emerging epigenetic model organism[END_REF]). He called these relations of the phenotype on an environmental gradient Phänotypenkurve. The combined relations of a phenotypic character and all environmental gradients that influences it, he defined as Reaktionsnorm or "norm of reaction". According to him, norms of reaction are specific to species and to lineages within species, they are heritable and based on (in his opinion are equal to) the genotype. He postulated that reaction norms can progressively be shifted over generations depending on the culture conditions of daphnia [START_REF] Woltereck | Weitere experimentelle Unter-suchungen uber Artveranderung, speziell uber das Wesen quantitativer Artunterschiede bei Daphniden[END_REF]. Later, in his 1932 textbook (Woltereck was a lecturer at the University of Leipzig), he extended this view to the notion that species should be defined by identical norms of reaction [START_REF] Woltereck | Grundzüge Einer Allgemeinen Biologie[END_REF]. This is a remarkable concept in the light of current difficulties to define species boundaries by phenotypic similarity, reproductive isolation or DNA sequence similarity. He also expanded the concept of the norm of reaction to three types of norms: 1st order (Modifikationen), 2nd order (Kombinationen), and 3rd order (Dauerinduktion and gene mutations). Modifikation was a textbook term in the 1920-30s and is equivalent to phenotypic variation. We will focus here on the 3rd order norms of reaction. Woltereck borrowed the term Dauerinduktion from Victor Jollos who had coined in the early 1900s; the term Dauermodifikation or "enduring modifications" (Jollos 1939), to describe phenotypic changes that could be provoked by environmental stimuli, would persist for a few generations and then revert. Interestingly, Woltereck considered enduring modifications and gene mutations somehow similar. Nevertheless, he proposed that the molecular basis would be different. Mutations occurred in genes, while enduring modifications were based on something he called the Matrix. He suggested that this matrix was associated with the chromosomes ("… chromosomes are matrix plus gene…"), that it was heritable, changed during development of the organisms, and that changes of the matrix could be simple chemical substitutions of an unknown, but probably polymeric molecule. (More on Woltereck's work at https:// embryo.asu.edu/pages/richard-wolterecks-conceptreaktionsnorm and [START_REF] Nicoglou | Epigenetics: A way to bridge the gap between biological fields. Studies in History and Philosophy of Science Part C Riessen H (2011) Predator-induced life history shifts in Daphnia: A synthesis of studies using meta-analysis[END_REF]). The phenomenon that organisms change their appearance as a function of environmental cues and/or during development is today rather called phenotypic plasticity, a term introduced in the 1960s. Mayr [START_REF] Mayr | The concept of plasticity in the history of the nature-nurture debate in the early twentieth century[END_REF] used "polyphenism" to distinguish environmentally induced phenotypic variation from those that he believed were genetically determined (polymorphisms). Two years later, Bradshaw termed the amount by which the expression of an individual genotype c a n b e m o d i f i e d b y i t s e n v i r o n m e n t a s "plasticity" [START_REF] Bradshaw | Evolutionary Significance of Phenotypic Plasticity in Plants[END_REF]) and discussed the importance of plasticity for evolution. Nowadays, the importance of developmental and environmental plasticity for the generation of phenotypic novelty is still a matter of lively scientific discussion [START_REF] Levis | Phenotypic plasticity, canalization, and the origins of novelty: Evidence and mechanisms from amphibians[END_REF]. But it is increasingly recognized that enduring phenotypic plasticity requires memory effects that can be related to epigenetic mechanisms. The definition of what is epigenetic depends very much on the scientific context in which the term is used [START_REF] Nicoglou | Epigenetics: A way to bridge the gap between biological fields. Studies in History and Philosophy of Science Part C Riessen H (2011) Predator-induced life history shifts in Daphnia: A synthesis of studies using meta-analysis[END_REF]. Here we will use it for any chromatin modification affecting gene expression, whether it is heritable or not [START_REF] Nicoglou | Epigenetics: A way to bridge the gap between biological fields. Studies in History and Philosophy of Science Part C Riessen H (2011) Predator-induced life history shifts in Daphnia: A synthesis of studies using meta-analysis[END_REF]) and we will show that it is related to Woltereck's matrix. In the last two decades, several studies have started to identify the molecular basis of such a matrix including noncoding RNAs, covalent modifications at the histone tails and DNA methylation. All of these mechanisms together constitute the epigenetic information that allows the remodeling (and maintenance) of chromatin structure and ultimately of phenotypes under environmental influence. In this regard, the global level of DNA methylation of Daphnia magna was found to be largely affected after exposure to abiotic (e.g. Zinc; [START_REF] Vandegehuchte | Gene transcription and higher-level effects of multigenerational Zn exposure in Daphnia magna[END_REF])) and biotic (toxic cyanobacterium Microcystis aeruginosa; [START_REF] Asselman | Bisulfite Sequencing with Daphnia Highlights a Role for Epigenetics in Regulating Stress Response to Microcystis through Preferential Differential Methylation of Serine and Threonine Amino Acids[END_REF])) environmental toxicants, or to irradiation (Trijau et al. 2018). However, no study has yet investigated the effect of environmental stimuli on the genome-wide chromatin structure. Here we argue that what Woltereck called the matrix is nowadays chromatin structure; the bearer of the overall epigenetic information including all epigenetic marks and their complex interactions. Here, we adapted an ATAC-Seq (Assay for Transposase Accessible Chromatin with high-throughput sequencing) [START_REF] Buenrostro | Transposition of native chromatin for fast and sensitive epigenomic profiling of open chromatin, DNAbinding proteins and nucleosome position[END_REF] protocol to characterise the overall genome-wide chromatin structure of Daphnia pulex in the context of the iconic complex defense response to predation. ATAC-seq works similarly as DNase-seq (DNase I hypersensitive sites with highthroughput sequencing) [START_REF] Song | DNase-seq: a high-resolution technique for mapping active gene regulatory elements across the genome from mammalian cells[END_REF], and determines which genomic regions are accessible to Tn5 transposase (i.e. open chromatin regions), especially the regulatory regions. Tn5 transposase inserts Illumina adapter ! of ! sequences upon accessing the chromatin, which removes the need for additional steps to make the sequencing libraries later. This simple and efficient protocol reduces the enables starting material required, compared to DNase-seq. It also avoids many other steps such as the interaction with antibodies (e.g. ChIP-seq) or chemical treatment (e.g. FAIRE-seq, WGBS) that might introduce bias. Our results show: (i) that ATAC-seq can be used to characterize chromatin structures of individuals even those that are small and thus with few biological material, making it possible to determine epigenetic polymorphisms relatively easily and at reasonable cost in full populations; and (ii) we deliver evidence that chromatin structure changes upon stimuli from the environment (figure 1).

This study therefore describes the classical experimental system postulated by Richard Woltereck 100 years ago: the adaptive morphological phenotypic plasticity of daphnia.

Results

ATAC-Seq can be used on individual Daphnia

Our ATAC-seq procedure delivered reproducible chromatin profiles for individual daphnia. Projection of ATAC-seq reads on a metagene profile indicated that Tn5 accessible and thus presumably open chromatin structure occurs at the TSS and in gene bodies (Figure 2, suppl. figure 1).

We started by comparing populations sampled at the beginning of the experiment (start) to the unexposed (control) population at the end of the exposure time of the experiment. Clustering algorithms built into DESeq2 were used to produce a graphical representation of sample-tosample distances based on the similarity of their ATAC-Seq patterns (Figure 3). These data indicate that there are 2,362 local differences (3.6% of all 66,194 identified ATAC enrichment regions) at an FDR of 0.05 between the start and the control population (p-value adjusted for multiple testing with the Benjamini-Hochberg procedure). This suggest that within 20 days (2-5 generations) there was either (i) epigenetic drift from 'start' to 'control' or (ii) epimutations were induced and/or selected by changes in the water tank environment from 'start' to 'control'.

Exposure to predator cues leads to morphological differences in Daphnia

Our results show that on average, the (LL-SL)/SL ratio calculated for daphnia from the stress treatment (N = 14; Mean = 0.24 ± 0.072) was significantly higher than that of daphnia from the control treatment (N = 12; Mean = 0.15 ± 0.039; Mann-Whitney U Test, U = 19, Z = -3.32, P < 0.001) (Figure 4). This result confirms the expected induction of anti-predatory morphs in the stress treatment. It is noteworthy that the quantified morphological response to predation pressure observed in the stress treatment most likely reflects a more general response of stressed daphnia including morphological, physiological and behavioural changes [START_REF] Boersma | Environmental stress and local adaptation in Daphnia magna[END_REF] Our first intention in comparing daphnia from the two experimental treatments ! of ! was to confirm that we effectively induced a global response in stressed individuals, these responses having been otherwise much better documented previously [START_REF] Riessen | Predator-induced life history shifts in Daphnia: a synthesis of studies using meta-analysis[END_REF])

Exposure to predator cues leads to differences in chromatin structure between exposed (stressed) and unexposed (control) Daphnia

Using the DESeq2 procedure described above for 'start' vs. 'control' we identified 66,194 differences between 'control' and 'stressed'. This is by far too many, and indeed, shifts in MA plots (not shown) indicated that the assumption that is underlying the algorythm used in DESeq2 and the requires that most sites do not change, was violated. Metagene profiles, using the same number of aligned reads over the entire genome, lend further support to the finding that 'stressed' samples had on average fewer reads over genes than 'control' samples indicating major changes in chromatin structure (Figure 5).

This also means that there is a large number of regions for which no reads could be recovered in the stressed samples. This is not due to a general lower accessibility of Tn5 to the cells and nuclei because of a thicker cuticle or a similar phenotypic trait because the insert size distribution of start, control and stressed populations are similar (Supplementary file 2). If DNA was more inaccessible in the stressed population we would expect longer fragments. To cope with the general decrease of ATAC-Seq reads in the stressed population, we resorted to ChromstaR, a HMM based software that was developed for ChIP-Seq analysis but that in principle can also be used for ATAC-Seq and is probably less sensitive to zero values. Under the constraints of numerous instances of an absence of data, ChromstaR identified 87 regions that are different between start and control, and stress. All were visually inspected using MACS2 average profiles, normalised by the same number of aligned reads over the genome. Among these 87 regions, ATAC signal was down in stressed samples compared to 'control and start' in 45 regions (52%), down in 'stress and control' compared to 'start' in 16 (18%), up in 'stress and control' in 3 (3.4%), and down in 'control' in only 1 (1.1%). Seven regions showed a heterogenous pattern on ATAC signals. In 15 regions differences were considered too weak (17%) suggesting that fine tuning of ChromstaR parameters might be necessary (Supplementary file 2). These results are in line with a general decrease in ATAC signal in the stressed samples, i.e. chromatin becomes less accessible and/or less heterogenous. It is interesting to note that for 20 regions adjacent ATAC signals (less than 2kb apart) were detected, lending further support to the idea that chromatin structure changes occur in a controlled fashion.

Clustering of the samples clearly regroups control and stressed samples (Figure 6). Another way to cope with presence of many zeroes that could produce a difference between two groups simply because zeroes in one group turn out to be very small values in the other, is to use log transformation; setting an arbitrary low threshold level of accessibility that we do not consider very different from zero. Here we transformed the data with log10(t+x), where t is the threshold of 0.1 and x is the ATAC-seq read count. Doing so we see again that 'stressed' are very different from 'controls': the distribution has many very small values (including many true zeroes = log10(t+x) = -1) and 'stress' mode is slightly shifted to the left. Given that we used normalization, this must be compensated by a few sequences with very high numbers of ! of ! reads (not visible but each counts a lot in the normalization). This suggests that under stress a few regions have many more reads than in controls and as a counterpart, many regions with relatively low number of reads have slightly less reads. By plotting transformed ATAC-Seq read counts of 'stressed' vs 'control' we see that there are two clouds of points: (i) those regions that have many more reads in stressed than in controls (+1-2 log10units = 10 -100fold change) and (ii) under the 1:1 stressed-control line those regions that are slightly less represented in the 'stressed' than in the 'controls' (Figure 6). Regions identified by ChromstaR are present in both clouds (Figure 7).

We therefore conclude that stress modifies the distribution of the numbers of reads drastically: a few hundred regions are much more represented (i.e. Tn5 accessible) in stressed than in control chromatin. This could reflect the fact that under stress these regions become accessible in many more tissues than in control conditions, thus they are captured many more times by the ATAC-seq. As a counterpart, the proportional representation of most other regions slightly decreases (fold change approximately ½ = -0.3 log10 units) but remain generally proportional to their value in controls.

Competition for sequencing (PCR amplification selects for the many reads from highly accessible regions) and normalization (divide by the total number of sequences) can be responsible for this.

Discussion

We report here a very fast and straightforward method to map the chromatin status of individuals using small amounts of input biological material [START_REF] Augusto | A simple ATAC-seq protocol for population epigenetics[END_REF]).

The technique is very robust and we have been using it for more than a year now on different species e.g. adult worms of the parasite Schistosoma mansoni. The technique was successfully used in the framework of a summer school for field ecologists, some of them with no training in molecular biology. The technique avoids many caveats that are involved with the use of antibody-based methods [START_REF] Egelhofer | An assessment of histone-modification antibody quality[END_REF] and is roughly 6 times faster. In our hands, there was no problem with mitochondrial contamination which is sometimes observed with other ATAC-seq methods. However, it also has some drawbacks: when using aquatic organisms, we observed DNA pollution from other species than the model species/species of interest. It is thus necessary to carefully wash the samples in DNA-free water. In addition, organisms should not be fed a couple of days before the ATAC experiment is performed. Another, inherent weakness of the method is that it provides just a positive readout of Tn5 accessible. These regions and considered nuleosome-free and presumably euchromatic. Absence of ATAC-Seq reads is generally considered as signal for inaccessible, and therefore heterochromatic regions. However, as with any method, the absence of proof is not proof of absence. This caveat is of course shared with any technique that relies on enzymatic accessibility such as DNA footprint, DNAse-seq or FAIRE-seq. It would be desirable to develop techniques that also provide a positive display of heterochromatic regions and without any use of antibodies. Notwithstanding these caveats, due to its minimal training requirements, low starting material as input and price advantage over other techniques, ATAC-seq can be used to develop fast epigenotyping approaches in populations similar to what is done routinely today in population genetics.

We estimate here the epimutation rate to be at least in the order of magnitude of 10 -3 which is in line to earlier findings (van der Graaf et al. 2015) [START_REF] Roquis | Frequency and mitotic heritability of epimutations in Schistosoma mansoni[END_REF]. However, we also realize that the current analysis methods are not suitable if strong, global changes in chromatin structure occurs. As for genetic analyses, the underlying assumptions of algorithms is that (epi)mutations are rare events. This prompts a need to develop new analysis methods that take large genome wide modifications of the chromatin structure into account. HMM based methods or our transformation method are promising starting points for this purpose.

The development of defensive crests upon exposure to kairomones from predators has been studied in great detail in several Daphnia species. It's developmental dynamics (e.g. [START_REF] Weiss | Predator-induced defences in Daphnia longicephala: location of kairomone receptors and timeline of sensitive phases to trait formation[END_REF]) and even the genes that are differently expressed (e.g. [START_REF] Rozenberg | Transcriptional profiling of predatorinduced phenotypic plasticity in Daphnia pulex[END_REF]) are now known. It is also recognized that genetic, non-genetic and environmental elements interact to bring about phenotypic variation in daphnia populations [START_REF] Harney | Offspring development and life-history variation in a water flea depends upon clone-specific integration of genetic, nongenetic and environmental cues[END_REF], a phenomenon that is probably applicable to all eukaryotes and that we have recently conceptualized as a systems biology view on inheritance [START_REF] Cosseau | Epi)genetic Inheritance in Schistosoma mansoni: A Systems Approach[END_REF]. Daphnia possess bearers of epigenetic information such as modified histones [START_REF] Robichaud | The Epigenetic Repertoire of Daphnia magna Includes Modified Histones[END_REF], and DNA methylation [START_REF] Kvist | Pattern of DNA Methylation in Daphnia: Evolutionary Perspective[END_REF] of the classical mosaic type [START_REF] Aliaga | Universality of the DNA methylation codes in Eucaryotes[END_REF]. Despite the the fact that the idea of a matrix was known when the term 'phenotypic plasticity' was formalised, it remains surprising that, to date, the link between Woltereck's matrix and the chromatin has not been explicitly made. Maybe because it was too evident, or maybe because the idea that heritable units are composed of several elements and not only DNA fragments (in Woltereck's words "… chromosomes are matrix plus gene…") is still not entirely accepted by the scientific community. The matrix concept provides a clear key to understanding how organisms can interpret environmental cues and change their phenotype over time spans that are beyond the duration of the cue. In terms of systems biology, the capacity to interpret these cues is the 'emerging ! of ! property' of the inheritance system that is composed of genotype and epigenotype (and potentially cytoplasmic elements and microorganisms). It also allowed eukaryotic cells to generate complexity and thus the symbiontic acquisition of histone-based chromatin organization was probably critical for the evolution of eukaryotic complex cells [START_REF] Brunk | Archaeal Histone Contributions to the Origin of Eukaryotes[END_REF].

In conclusion, we show here that moderate changes in the environment (during the 20 days, i.e. 2-5 generations, from 'start' where daphnia where introduced into their new water tanks to 'control' ) are accompanied by roughly 4% of epigenetic modifications. When strong environmental cues, such as predator presence, are applied, the chromatin structure is reorganised much more profoundly and many regions become inaccessible to Tn5.

Materials and Methods

Daphnia culture and experimental design

A batch of ~300 commercial Daphnia pulex was obtained f r o m a c o m m e r c i a l s u p p l i e r ( A q u a l i m e n t : http:// www.aqualiment.eu/). At their arrival, daphnia were immediately split into two sets of equal size (~ 150 x 2) and placed in two independent experimental tanks (i.e. initial density of 75 ind.L -1 ), hereafter called the 'stress' and the 'control' tanks. Each experimental tank consisted in a2-L plastic aquaria (L x l x h = 18 x12 x 11 cm) supplied with clean water, inside of which a floating plastic fish breeding isolation box (L x l x h = 12,5 x 8 x7 cm) was placed (Figure 1). These isolation boxes are transparent with a series of 1 mm cracks on the bottom wall to allow water connection between the tanks and inside the isolation box. Daphnia were acclimated in their respective experimental tanks out of the isolation box for 20 days prior to starting the experiment. This lag time before the experiment also allowed the production of new daphnia offspring born in our experimental setup. During this acclimating period, only negligible mortality was observed and newly hatched daphnia were observed in the two experimental tanks. After this 20-day acclimating period, a predator (i.e. a guppy fish previously trained to eat daphnia) was introduced into the isolation box of one experimental tank during 15 days (i.e. hereafter called the 'stress treatment', compared to the 'control treatment').

During the experiment the fish was fed every other day with 10 daphnia collected alternatively from the stress and the control tank (i) to avoid subsequent biases in density between the experimental treatments and (ii) to account for a possible effect of daphnia sampling on congeners' responses. Daphnia sampling for fish feeding was achieved using a sterile 3-ml plastic transfer pipet. This experimental setup allowed the daphnia of the stress treatment to experience an indirect predation pressure (i.e. without predation risk) through a direct visual contact with the predator and an olfactory contact with environmental cues released by the predator. Overall the experiment, the daphnia and the predator were maintained at room temperature following the natural photoperiod and the former were fed ad libitum with clean phytoplancton (i.e. chlorellasp.) reared in our lab facilities.

Sampling and morphometry

Four daphnia were sampled during the 20 days acclimating period (called herein 'start' population) and immediately processed for ATAC-Seq. At day 15 of stress treatment (2-5 generations), 12 and 14 living daphnia were respectively sampled from each of the control and stress treatment by pipetting through a 1 mL automatic pipette with enlarged openings of the pipetting tips and disposed on microscopic slides for dark field microscopy. To avoid experimenter bias 10 different persons sampled at least one control and one stressed daphnia. Each daphnia was observed and photographed under a stereo microscope (Leica EZ4) at a 100fold magnification using the Leica application suite LAS EZ Version 3.4.0.

From each picture two body lengths were measured (Figure 8): the short length (SL=from the middle of the eye to the base of the apical spine) and the long length (LL=from the middle of the eye to the tip of the apical spine). Finally, each measured animal was then individually transferred to a 1.5 mL Eppendorf tube and was immediately processed for ATAC-seq library preparation. To check for morphological response of daphnia to predation pressure we compared the individual ratio of (LL-SL)/SL of each treatment with a student t-test using Excel and http://www.estimationstats.com/#/ analyze/two-independent-groups.

ATAC-Seq

The ATAC-Seq protocol we used is based on Corces et al., [START_REF] Corces | Lineagespecific and single-cell chromatin accessibility charts human hematopoiesis and leukemia evolution[END_REF]) with some modifications [START_REF] Augusto | A simple ATAC-seq protocol for population epigenetics[END_REF]. All water was removed from the daphnia containing tubes through pipetting. Daphnia were washed once with 50 µl cold PBS and all liquid was then removed by pipetting. 22 µl nuclease free water, 25 µl 2x TD buffer (Illumina FC-121-1030), 2.5 µl TDE (Tn5 Illumina FC-121-1030) and 0.5 µl 1% IGEPAL CA-630 (Sigma-Aldrich, cat. no. I8896) were added and mixed by pipetting 10 times to disrupt cells. Reaction mixtures were incubated at 37°C for 30 min at 300 rpm agitation. Transposed DNA was immediately purified using a QIAquick PCR Purification Kit (#28106), and purified DNA was eluted into 10 µl of elution buffer (10 mMTris-HCl, pH 8). Libraries were PCR amplified using Promega GoTaq2, universal Ad1_noMX primer and index primer Ad2.* (http:// www.nature.com/nmeth/journal/v13/n11/extref/nmeth.3999-S5.xlsx) (each 1.25 µM) that was different for each individual daphnia, 10 µl of DNA in a total volume of 50 µl. Preamplification was done at 98°C for 30 sec, then five cycles of 98°C for 10 sec, 63°C for 30 sec, 72°C for 1 min. 5 µl of this PCR mixture was used for qPCR analysis to determine the number of additional amplification cycles. Relative fluorescence was plotted versus cycle number and the cycle number that corresponds to one-third of the maximum fluorescent intensity was used for additional PCR amplification. After PCR, size-selection at 300 bp was done on an IP-Star system with Ampure XP beads. Quality and quantity of libraries were checked with an Agilent Bioanalyzer High Sensitivity DNA Assay and library were sequenced on a NextSeq550 High Output Flowcell as paired-end and 75 bp. A detailed step-by-step protocol in Augusto et al 2019.

Detection of chromatin structure differences

Figure 1 :

 1 Figure 1: Experimental design used in this study. Daphnia were put into a water tank and allowed to acclimate (start population). Then, two experimental tanks were set up following strictly the same design. The only difference was the presence of a predator (a guppy trained to eat daphnia) in the floating plastic fish breeding isolation box in the stress treatment.

Figure 3 :Figure 2 :

 32 Figure 3: MA-Plot (top) and Principal component analysis of individual Daphnia based on their ATAC-Seq profiles (bottom). On the PCA every point represents an individual daphnia. Populations are color coded. Samples from the start (blue) and control population (red) cluster clearly.

Figure 4 :

 4 Figure 4: Boxplot of morphometric ratios of (LL-SL)/SL in control and stressed daphnia populations (control: N = 12; stress: N= 14).

Figure 5 :

 5 Figure 5: Combined metagene ATAC profiles of stressed and control daphnia populations. X-axis in base-pairs. TSS = Transcription start site, TES = transcription end site. Y-axis average enrichment of ATACseq reads over genes and upstream and downstream regions.

Figure 6 :

 6 Figure 6: Clustering of individual daphnia based on their ATAC-Seq profiles. Heat map indicating similarity in the HMM ChromstaR results. Generally samples from the stressed and the control populations each cluster together.

Figure 7 :

 7 Figure 7: Plot of transformed ATAC-Seq read counts of 'stressed' vs 'control'. Two point clouds of points: 1) at the top-left, those regions have many more reads in stressed than in controls (+1-2 log10units = 10 -100fold change), and 2) under the 1:1 stressed-control dotted line, those regions that are slightly less represented in the 'stressed' than in the 'controls'. Red dots (D) represent regions that were determined as differently accessible by ChromstaR HMM approach. ND all others.

  Sequence quality was checked with FastQC (http:// www.bioinformatics.babraham.ac.uk/projects/fastqc/). R e f e r e n c e g e n o m e w a s d o w n l o a d e d f r o m ftp:// ftp.ensemblgenomes.org/pub/metazoa/release-40/fasta/ daphnia_pulex/dna/Daphnia_pulex.V1.0.dna.toplevel.fa.gz , ! of ! 5 7

Figure 8 :

 8 Figure 8: Schematic representation of the measures taken on daphnia. SL = short length, LL = Long length.

Acknowledgments

These experiments were done in the framework of the RTP 3E summer school "Epigenetics for field ecologists" and received support from the CNRS.

c o r r e s p o n d i n g t o G e n B a n k a s s e m b l y a c c e s s i o n GCA_000187875.1. Alignment was done with Bowtie2 evoking the following parameters: bowtie2-align-s basic-0 -p 6 -x genome -N 1 -L 32 -i S,1,1.15 --n-ceil L,0,0.15 --dpad 15 --gbar 4 --end-to-end --score-min L,-0.6,-0.6. Uniquely aligned reads were retained by filtering the tag "XS:i:" that is absent in their alignement annotations. For visualisation of ATAC profiles all BAM files for each condition were merged, converted to header-free SAM, and downsampled with a custom script that draws random lines to 409,000 aligned reads. This corresponds to the condition with the lowest number of aligned reads. For analysis of individual daphnia PCR duplicates were removed with SamTools RmDup. Bedgraph files were generated with MACS2 using model building, lower fold bound of 5, upper fold bound 50, band width 300 bp, minimum FDR for peak detection of 0.05, an effective genome size of 150,000,000, and without calling broad regions. Bedgraphs were loaded into IGV for visual inspection. For analysis of individual daphnia, background correction was done with MACS bdgcmp. Bedgraph was converted into BigWig. The DeepTools suite was used for representation of metagene profiles based on this over 15,287 genes on the forward strand. Gene annotation files were downloaded from ftp:// ftp.ensemblgenomes.org/pub/metazoa/release-40/fasta/ daphnia_pulex/cds/Daphnia_pulex.V1.0.cds.all.fa.gz . More information is available at https://metazoa.ensembl.org/ Daphnia_pulex/Info/Annotation/ Two different approaches were used for further data analysis. One uses a combination of peakcalling with MACS2, extraction of read coverage in peaks with BEDtools, and DESeq2 for differential analysis. To detect all peak regions for all conditions, BAM files of control and stress conditions were merged and peakcalling was performed with MACS2 as described above. The number of reads overlapping peak regions was extracted with bedtools intersect -a peakfile.bed -b individual_bam_files.bam -header -wa -c, Columns 4 and 11, corresponding to peak-names and number of overlapping features, i.e. coverage were used as input for DESeq2. All analyses were done at the galaxy instance of the Labex CeMEB/IHPE (http://bioinfo.univperp.fr).

The second approach was based on Hidden-Markow-Models (HMM) implemented in ChromstaR (v.1.2.0) for genome-wide characterization of open chromatin landscape. On this approach control and stress condition were processed in two steps: (1) we fitted a univariate HMM over each ATAC-seq samples individually and (2) we performed a multivariate HMM over the combined ATAC-seq samples in each condition. For that, BAM files were processed under the differential mode, with a false discovery rate (FDR) cutoff of 0.05 and bin size of 500.

End Matter

Author Contributions and Notes R.A. and C.G. designed research, all authors performed research, P.D. wrote software, R.A., P.D. and C.G. analyzed data; and all authors wrote the paper. The authors declare no conflict of interest. This article contains supporting information online on NCBI SRA.


Abbas Chokor

Reine Talj

Moustapha Doumiati

Ali Charara

A Global Chassis Control System Involving Active Suspensions, Direct Yaw Control and Active Front Steering

Keywords: Global Chassis Control, Multilayer Control, Super-Twisting Sliding Mode Control, Fuzzy Logic, Active Suspension, Direct Yaw Control, Active Front Steering Global Chassis Control, Multilayer Control, Super-Twisting Sliding Mode Control, Fuzzy Logic, Active Suspension, Direct Yaw Control, Active Front Steering Global Chassis Control, Multilayer Control, Super-Twisting Sliding Mode Control, Fuzzy Logic, Active Suspension, Direct Yaw Control, Active Front Steering Global Chassis Control, Multilayer Control, Super-Twisting Sliding Mode Control, Fuzzy Logic, Active Suspension, Direct Yaw Control, Active Front Steering Global Chassis Control, Multilayer Control, Super-Twisting Sliding Mode Control, Fuzzy Logic, Active Suspension, Direct Yaw Control, Active Front Steering Global Chassis Control, Multilayer Control, Super-Twisting Sliding Mode Control, Fuzzy Logic, Active Suspension, Direct Yaw Control, Active Front Steering

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INTRODUCTION

Driving safety is a major challenge for our society. According to the "National Highway Traffic Safety Administration (NHTSA)" statistics, human errors commit almost 90% of road accidents as explained in [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF]. The integration of an Advanced Driving Assistance System (ADAS) in the vehicle permits to act in an appropriate way to avoid accidents, skidding and rollover. ADAS systems are formed by several single-actuator approaches that have been proposed and marketed, such as: Vehicle Stability Control (VSC) or Electronic Stability Program (ESP) including Direct Yaw Control (DYC), Anti-lock Braking System (ABS) and others, to enhance the vehicle handling and stability; Active Front Steering (AFS) to improve the vehicle maneuverability or lane keeping; and Active Suspensions (AS) to improve comfort and road holding. Current and future intelligent vehicles are incorporating more sophisticated chassis control systems, known by Global Chassis Control system (GCC). GCC is an integrated vehicle chassis control system that coordinates several ADAS systems to improve the overall vehicle performance. It consists of creating a global performance efficient controller from sub-controllers which operate independently and have independent local objectives. Research in the GCC field mainly focus on the coordination of the AFS with the DYC, to improve the vehicle stability and maneuverability [START_REF] Karbalaei | A new intelligent strategy to integrated control of afs/dyc based on fuzzy logic[END_REF]], [START_REF] Poussot-Vassal | Robust vehicle dynamic stability controller involving steering and braking systems[END_REF]], and [START_REF] Doumiati | Integrated vehicle dynamics control via coordination of active front steering and rear braking[END_REF]]. The active (semiactive) suspensions were introduced in the GCC strategy to improve the ride comfort and road holding [START_REF] Savaresi | Semi-active suspension control design for vehicles[END_REF]],

This work was supported by the Hauts-de-France Region and the European Regional Development Fund (ERDF). [START_REF] Yoon | Design of an unified chassis controller for rollover prevention, manoeuvrability and lateral stability[END_REF]] and [START_REF] Akhmetov | Global Chassis Control for active safety of heavy vehicles[END_REF]]. Recently, the GCC strategy has been evolved to coordinate different subcontrollers. Indeed, the studies on the active (semi-active) suspensions are enlarged to control the vehicle stability (lateral and vertical). Many research studies as [START_REF] Fergani | LPV/H ∞ suspension robust control adaption of the dynamical lateral load transfers based on a differential algebraic estimation approach[END_REF], [START_REF] Chen | Rollover prevention using active suspension system[END_REF], [START_REF] Vu | Enhancing roll stability of heavy vehicle by lqr active anti-roll bar control using electronic servo-valve hydraulic actuators[END_REF], [START_REF] Yao | Lateral stability control based on the roll moment distribution using a semiactive suspension[END_REF], and [START_REF] Mirzaei | Fuzzy scheduled optimal control of integrated vehicle braking and steering systems[END_REF] propose to control the vertical load transfer when cornering, or minimizing the vertical displacements of the unsprung masses, known as the most influencing factors on the lateral tires forces, and thus on the lateral stability. The main goal of the GCC system developed in this paper is to enhance the overall vehicle performance i.e. maneuverability, stability (lateral and vertical), and ride comfort. Fig. 1 depicts the general architecture of the proposed GCC. It consists of an AFS controller which will be developed to generate an additional steering angle, mainly to improve the maneuverability and enhance the lateral stability; a DYC controller which will be developed to generate a yaw moment that controls and guarantees the lateral stability of the vehicle; and an AS controller which will be developed to generate active suspension forces to improve ride comfort, vertical stability and lateral stability. The paper contributions are as follows:

• single-input single-output super-twisting sliding mode controllers are developed to control the active suspensions, the DYC, and the AFS in the presence of modeling errors, external disturbances and exogenous inputs. • new objectives are achieved by the AS controller usually developed for ride comfort. It is exploited to improve the vertical stability (rollover avoidance) and lateral stability (lateral skidding avoidance). General improvements are

INTRODUCTION

Driving safety is a major challenge for our society. According to the "National Highway Traffic Safety Administration (NHTSA)" statistics, human errors commit almost 90% of road accidents as explained in [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF]. The integration of an Advanced Driving Assistance System (ADAS) in the vehicle permits to act in an appropriate way to avoid accidents, skidding and rollover. ADAS systems are formed by several single-actuator approaches that have been proposed and marketed, such as: Vehicle Stability Control (VSC) or Electronic Stability Program (ESP) including Direct Yaw Control (DYC), Anti-lock Braking System (ABS) and others, to enhance the vehicle handling and stability; Active Front Steering (AFS) to improve the vehicle maneuverability or lane keeping; and Active Suspensions (AS) to improve comfort and road holding. Current and future intelligent vehicles are incorporating more sophisticated chassis control systems, known by Global Chassis Control system (GCC). GCC is an integrated vehicle chassis control system that coordinates several ADAS systems to improve the overall vehicle performance. It consists of creating a global performance efficient controller from sub-controllers which operate independently and have independent local objectives. Research in the GCC field mainly focus on the coordination of the AFS with the DYC, to improve the vehicle stability and maneuverability [START_REF] Karbalaei | A new intelligent strategy to integrated control of afs/dyc based on fuzzy logic[END_REF]], [START_REF] Poussot-Vassal | Robust vehicle dynamic stability controller involving steering and braking systems[END_REF]], and [START_REF] Doumiati | Integrated vehicle dynamics control via coordination of active front steering and rear braking[END_REF]]. The active (semiactive) suspensions were introduced in the GCC strategy to improve the ride comfort and road holding [START_REF] Savaresi | Semi-active suspension control design for vehicles[END_REF]],

This work was supported by the Hauts-de-France Region and the European Regional Development Fund (ERDF). [START_REF] Yoon | Design of an unified chassis controller for rollover prevention, manoeuvrability and lateral stability[END_REF]] and [START_REF] Akhmetov | Global Chassis Control for active safety of heavy vehicles[END_REF]]. Recently, the GCC strategy has been evolved to coordinate different subcontrollers. Indeed, the studies on the active (semi-active) suspensions are enlarged to control the vehicle stability (lateral and vertical). Many research studies as [START_REF] Fergani | LPV/H ∞ suspension robust control adaption of the dynamical lateral load transfers based on a differential algebraic estimation approach[END_REF], [START_REF] Chen | Rollover prevention using active suspension system[END_REF], [START_REF] Vu | Enhancing roll stability of heavy vehicle by lqr active anti-roll bar control using electronic servo-valve hydraulic actuators[END_REF], [START_REF] Yao | Lateral stability control based on the roll moment distribution using a semiactive suspension[END_REF], and [START_REF] Mirzaei | Fuzzy scheduled optimal control of integrated vehicle braking and steering systems[END_REF] propose to control the vertical load transfer when cornering, or minimizing the vertical displacements of the unsprung masses, known as the most influencing factors on the lateral tires forces, and thus on the lateral stability. The main goal of the GCC system developed in this paper is to enhance the overall vehicle performance i.e. maneuverability, stability (lateral and vertical), and ride comfort. Fig. 1 depicts the general architecture of the proposed GCC. It consists of an AFS controller which will be developed to generate an additional steering angle, mainly to improve the maneuverability and enhance the lateral stability; a DYC controller which will be developed to generate a yaw moment that controls and guarantees the lateral stability of the vehicle; and an AS controller which will be developed to generate active suspension forces to improve ride comfort, vertical stability and lateral stability. The paper contributions are as follows:

• single-input single-output super-twisting sliding mode controllers are developed to control the active suspensions, the DYC, and the AFS in the presence of modeling errors, external disturbances and exogenous inputs. Research in the GCC field mainly focus on the coordination of the AFS with the DYC, to improve the vehicle stability and maneuverability [START_REF] Karbalaei | A new intelligent strategy to integrated control of afs/dyc based on fuzzy logic[END_REF]], [START_REF] Poussot-Vassal | Robust vehicle dynamic stability controller involving steering and braking systems[END_REF]], and [START_REF] Doumiati | Integrated vehicle dynamics control via coordination of active front steering and rear braking[END_REF]]. The active (semiactive) suspensions were introduced in the GCC strategy to improve the ride comfort and road holding [START_REF] Savaresi | Semi-active suspension control design for vehicles[END_REF]],

This work was supported by the Hauts-de-France Region and the European Regional Development Fund (ERDF). [START_REF] Yoon | Design of an unified chassis controller for rollover prevention, manoeuvrability and lateral stability[END_REF]] and [START_REF] Akhmetov | Global Chassis Control for active safety of heavy vehicles[END_REF]]. Recently, the GCC strategy has been evolved to coordinate different subcontrollers. Indeed, the studies on the active (semi-active) suspensions are enlarged to control the vehicle stability (lateral and vertical). Many research studies as [START_REF] Fergani | LPV/H ∞ suspension robust control adaption of the dynamical lateral load transfers based on a differential algebraic estimation approach[END_REF], [START_REF] Chen | Rollover prevention using active suspension system[END_REF], [START_REF] Vu | Enhancing roll stability of heavy vehicle by lqr active anti-roll bar control using electronic servo-valve hydraulic actuators[END_REF], [START_REF] Yao | Lateral stability control based on the roll moment distribution using a semiactive suspension[END_REF], and [START_REF] Mirzaei | Fuzzy scheduled optimal control of integrated vehicle braking and steering systems[END_REF] propose to control the vertical load transfer when cornering, or minimizing the vertical displacements of the unsprung masses, known as the most influencing factors on the lateral tires forces, and thus on the lateral stability. The main goal of the GCC system developed in this paper is to enhance the overall vehicle performance i.e. maneuverability, stability (lateral and vertical), and ride comfort. Fig. 1 depicts the general architecture of the proposed GCC. It consists of an AFS controller which will be developed to generate an additional steering angle, mainly to improve the maneuverability and enhance the lateral stability; a DYC controller which will be developed to generate a yaw moment that controls and guarantees the lateral stability of the vehicle; and an AS controller which will be developed to generate active suspension forces to improve ride comfort, vertical stability and lateral stability. The paper contributions are as follows:

• single-input single-output super-twisting sliding mode controllers are developed to control the active suspensions, the DYC, and the AFS in the presence of modeling errors, external disturbances and exogenous inputs. [START_REF] Karbalaei | A new intelligent strategy to integrated control of afs/dyc based on fuzzy logic[END_REF]], [START_REF] Poussot-Vassal | Robust vehicle dynamic stability controller involving steering and braking systems[END_REF]], and [START_REF] Doumiati | Integrated vehicle dynamics control via coordination of active front steering and rear braking[END_REF]]. The active (semiactive) suspensions were introduced in the GCC strategy to improve the ride comfort and road holding [START_REF] Savaresi | Semi-active suspension control design for vehicles[END_REF]],

This work was supported by the Hauts-de-France Region and the European Regional Development Fund (ERDF). [START_REF] Yoon | Design of an unified chassis controller for rollover prevention, manoeuvrability and lateral stability[END_REF]] and [START_REF] Akhmetov | Global Chassis Control for active safety of heavy vehicles[END_REF]]. Recently, the GCC strategy has been evolved to coordinate different subcontrollers. Indeed, the studies on the active (semi-active) suspensions are enlarged to control the vehicle stability (lateral and vertical). Many research studies as [START_REF] Fergani | LPV/H ∞ suspension robust control adaption of the dynamical lateral load transfers based on a differential algebraic estimation approach[END_REF], [START_REF] Chen | Rollover prevention using active suspension system[END_REF], [START_REF] Vu | Enhancing roll stability of heavy vehicle by lqr active anti-roll bar control using electronic servo-valve hydraulic actuators[END_REF], [START_REF] Yao | Lateral stability control based on the roll moment distribution using a semiactive suspension[END_REF], and [START_REF] Mirzaei | Fuzzy scheduled optimal control of integrated vehicle braking and steering systems[END_REF] propose to control the vertical load transfer when cornering, or minimizing the vertical displacements of the unsprung masses, known as the most influencing factors on the lateral tires forces, and thus on the lateral stability. The main goal of the GCC system developed in this paper is to enhance the overall vehicle performance i.e. maneuverability, stability (lateral and vertical), and ride comfort. Fig. 1 depicts the general architecture of the proposed GCC. It consists of an AFS controller which will be developed to generate an additional steering angle, mainly to improve the maneuverability and enhance the lateral stability; a DYC controller which will be developed to generate a yaw moment that controls and guarantees the lateral stability of the vehicle; and an AS controller which will be developed to generate active suspension forces to improve ride comfort, vertical stability and lateral stability. The paper contributions are as follows:

• single-input single-output super-twisting sliding mode controllers are developed to control the active suspensions, the DYC, and the AFS in the presence of modeling errors, external disturbances and exogenous inputs. Current and future intelligent vehicles are incorporating more sophisticated chassis control systems, known by Global Chassis Control system (GCC). GCC is an integrated vehicle chassis control system that coordinates several ADAS systems to improve the overall vehicle performance. It consists of creating a global performance efficient controller from sub-controllers which operate independently and have independent local objectives. Research in the GCC field mainly focus on the coordination of the AFS with the DYC, to improve the vehicle stability and maneuverability [START_REF] Karbalaei | A new intelligent strategy to integrated control of afs/dyc based on fuzzy logic[END_REF]], [START_REF] Poussot-Vassal | Robust vehicle dynamic stability controller involving steering and braking systems[END_REF]], and [START_REF] Doumiati | Integrated vehicle dynamics control via coordination of active front steering and rear braking[END_REF]]. The active (semiactive) suspensions were introduced in the GCC strategy to improve the ride comfort and road holding [START_REF] Savaresi | Semi-active suspension control design for vehicles[END_REF]],

This work was supported by the Hauts-de-France Region and the European Regional Development Fund (ERDF). [START_REF] Yoon | Design of an unified chassis controller for rollover prevention, manoeuvrability and lateral stability[END_REF]] and [START_REF] Akhmetov | Global Chassis Control for active safety of heavy vehicles[END_REF]]. Recently, the GCC strategy has been evolved to coordinate different subcontrollers. Indeed, the studies on the active (semi-active) suspensions are enlarged to control the vehicle stability (lateral and vertical). Many research studies as [START_REF] Fergani | LPV/H ∞ suspension robust control adaption of the dynamical lateral load transfers based on a differential algebraic estimation approach[END_REF], [START_REF] Chen | Rollover prevention using active suspension system[END_REF], [START_REF] Vu | Enhancing roll stability of heavy vehicle by lqr active anti-roll bar control using electronic servo-valve hydraulic actuators[END_REF], [START_REF] Yao | Lateral stability control based on the roll moment distribution using a semiactive suspension[END_REF], and [START_REF] Mirzaei | Fuzzy scheduled optimal control of integrated vehicle braking and steering systems[END_REF] propose to control the vertical load transfer when cornering, or minimizing the vertical displacements of the unsprung masses, known as the most influencing factors on the lateral tires forces, and thus on the lateral stability. The main goal of the GCC system developed in this paper is to enhance the overall vehicle performance i.e. maneuverability, stability (lateral and vertical), and ride comfort. Fig. 1 depicts the general architecture of the proposed GCC. It consists of an AFS controller which will be developed to generate an additional steering angle, mainly to improve the maneuverability and enhance the lateral stability; a DYC controller which will be developed to generate a yaw moment that controls and guarantees the lateral stability of the vehicle; and an AS controller which will be developed to generate active suspension forces to improve ride comfort, vertical stability and lateral stability. The paper contributions are as follows:

• single-input single-output super-twisting sliding mode controllers are developed to control the active suspensions, the DYC, and the AFS in the presence of modeling errors, external disturbances and exogenous inputs. [START_REF] Karbalaei | A new intelligent strategy to integrated control of afs/dyc based on fuzzy logic[END_REF]], [START_REF] Poussot-Vassal | Robust vehicle dynamic stability controller involving steering and braking systems[END_REF]], and [START_REF] Doumiati | Integrated vehicle dynamics control via coordination of active front steering and rear braking[END_REF]]. The active (semiactive) suspensions were introduced in the GCC strategy to improve the ride comfort and road holding [START_REF] Savaresi | Semi-active suspension control design for vehicles[END_REF]],

This work was supported by the Hauts-de-France Region and the European Regional Development Fund (ERDF). [START_REF] Yoon | Design of an unified chassis controller for rollover prevention, manoeuvrability and lateral stability[END_REF]] and [START_REF] Akhmetov | Global Chassis Control for active safety of heavy vehicles[END_REF]]. Recently, the GCC strategy has been evolved to coordinate different subcontrollers. Indeed, the studies on the active (semi-active) suspensions are enlarged to control the vehicle stability (lateral and vertical). Many research studies as [START_REF] Fergani | LPV/H ∞ suspension robust control adaption of the dynamical lateral load transfers based on a differential algebraic estimation approach[END_REF], [START_REF] Chen | Rollover prevention using active suspension system[END_REF], [START_REF] Vu | Enhancing roll stability of heavy vehicle by lqr active anti-roll bar control using electronic servo-valve hydraulic actuators[END_REF], [START_REF] Yao | Lateral stability control based on the roll moment distribution using a semiactive suspension[END_REF], and [START_REF] Mirzaei | Fuzzy scheduled optimal control of integrated vehicle braking and steering systems[END_REF] propose to control the vertical load transfer when cornering, or minimizing the vertical displacements of the unsprung masses, known as the most influencing factors on the lateral tires forces, and thus on the lateral stability. The main goal of the GCC system developed in this paper is to enhance the overall vehicle performance i.e. maneuverability, stability (lateral and vertical), and ride comfort. Fig. 1 depicts the general architecture of the proposed GCC. It consists of an AFS controller which will be developed to generate an additional steering angle, mainly to improve the maneuverability and enhance the lateral stability; a DYC controller which will be developed to generate a yaw moment that controls and guarantees the lateral stability of the vehicle; and an AS controller which will be developed to generate active suspension forces to improve ride comfort, vertical stability and lateral stability. The paper contributions are as follows:

• single-input single-output super-twisting sliding mode controllers are developed to control the active suspensions, the DYC, and the AFS in the presence of modeling errors, external disturbances and exogenous inputs. also observed, e.g., the DYC will be less solicited, the vehicle speed will less drop, and others... • development of a decision layer that promotes/attenuates the local sub-controllers objectives. This layer monitors the dynamics of the vehicle, calculates and sends scheduled gains to the sub-controllers, based on fuzzy logic rules and a stability criterion.

ψ ref δ d δ d V x δ c C z U ij ×4 θ θ ref ϕ z - + + - Roll Ref Generator Data ( ψ , β , β ,θ ,ϕ , z , V x ...)
The paper structure is as follows: Section 2 develops the GCC system, starting by a review of the vehicle model, passing by the development of the sub-controllers to realize their local objectives and analyze the interactions between them, to finally develop the decision layer. Section 3 validates the proposed GCC system. Finally, the conclusions and the perspective works come in Section 4.

GLOBAL CHASSIS CONTROL SYSTEM

Vehicle model

A full vehicle nonlinear model has been already developed in [START_REF] Chokor | Active suspension control to improve passengers comfort and vehicle's stability[END_REF]. It combines the vertical, lateral, longitudinal, and tire/road contact (Dugoff model) sub-models, in addition to four wheels angular dynamics ω i j , with a 26 state variables gathered in the state vector X of (1) and shown in Fig. 2. The vertical model describes the roll θ , pitch φ , heave z, and unsprung masses z us,i j (on four wheels) dynamics. The lateral model describes the lateral motion y (in the vehicle body frame), yaw motion ψ, and side slip β dynamics. Finally, the longitudinal model describes the longitudinal dynamics x (in the vehicle body frame). The vehicle parameters and variables are given in Table 1. 2), ( 3), ( 4), ( 5) and (6). To be noted that equations ( 5) and ( 6) are linearized w.r.t the control input δ to facilitate their control. However, the GCC approach is validated on the Full vehicle model. θ

θ x ϕ y ψ z δ l f l r t f t r t f l f l r t r β ψ ⃗ V = ⃗ ẋ + ⃗ ẏ
= g θ (X) + f θ (X)M θ + d θ (X,t), (2) φ = g φ (X) + f φ (X)M φ + d φ (X,t), (3) z = g z (X) + f z (X)M z + d z (X,t), (4) ψ = g ψ (X) + f ψ,δ (X)δ + f ψ,C z (X)C z + d ψ (X,t), (5) β = g β (X) + f β ,δ (X)δ + f β ,C z (X)C z + d β (X,t).
(6) M θ , M φ , and M z represent respectively the active roll moment, active pitch moment, and active heave force, as intermediate control inputs. These inputs have to be generated at a lower level control by physical actuators, e.g. Active Suspensions AS forces U i j integrated on four corners. δ = δ d + δ c is the total steering angle at the front wheels, where δ d is the one provided by the driver and δ c is the one provided by the AFS controller. C z is the active yaw torque provided by the DYC controller. C z has to be generated at a lower level control as a differential braking on the rear wheels. g q (X), f v (X), f l,δ (X), and f l,C z (X) where q = {v, l}, v = {θ , φ , z} and l = { ψ, β } are nonlinear continuous functions detailed in Appendix A. d q (X,t) represent modeling errors and external disturbances supposed to be bounded as given in (7).

|d q (X,t)| ≤ D q ; q = {θ , φ , z, ψ, β }, (7) where D q are positive constant values. Note:1 -The lateral and longitudinal accelerations used later in the paper are in a fixed reference frame and are noted respectively by a y and a x . In modeling, a y and a x are constructed from ẋ, ẍ, ẏ, ÿ, ψ. V x used later in the paper is the time integral of a x .

-In real time control, the controlled variables ψ, φ and θ are measured by gyrometers and provided at the CG of the vehicle. θ and φ are estimated by time integration and could be provided by the Inertial Measurement Unit IMU -if available-. a y , a x and z are measured by accelerometers. ż, z are integrated from z. The side slip angle β and its derivative β could be estimated. Several observer approaches that suit the real time constraints implementation and vehicle dynamics have been proposed in

GCC sub-controllers

In order to develop robust individual controllers for the subsystems described by Equations ( 2), ( 3), ( 4), ( 5) and ( 6), dealing with the nonlinear behavior of the vehicle, and in the presence of unmodeled dynamics, external disturbances and exogenous inputs (for some cases), the super-twisting second order sliding mode theory as a robust model-based theory is chosen to control the sub-controllers AS, AFS, and DYC.

a) Super-twisting sliding mode controller:

In this Subsection, an overview of the super-twisting sliding mode control theory is presented. Used notations refers only to this subsection, unless mentioned in the other subsections. The super-Twisting algorithm is a second order sliding mode control that handles a relative degree equal to one. It generates the continuous control function that drives the sliding variable and its derivative to zero in finite time in the presence of smooth matched disturbances. Consider the system written as: ẋ = f (x,t) + g(x,t)u(t) (8) where u is the control input, x ∈ ℜ n the state vector, and f , g continuous functions. Let us define a sliding variable s of relative degree equal to one, and with a second derivative written as: s(s,t) = Φ(s,t) + ξ (s,t) u(t) (9) where Φ(s,t) and ξ (s,t) are unknown bounded signals. The control objective is to achieve the convergence to the sliding surface defined as s = 0. Only the knowledge of s is required in real time. Suppose that there exist positive constants S 0 , b min , b max , C 0 , U max such that ∀x ∈ ℜ n and |s(x,t)| < S 0 , the system satisfies the following conditions:

|u(t)| ≤ U max |Φ(s,t)| < C 0 0 < b min ≤ |ξ (s,t)| ≤ b max (10)
The sliding mode control law, based on the Super-Twisting algorithm, is given by:

u(t) = u 1 + u 2 u 1 = -α 1 |s| τ sign(s), τ ∈]0, 0.5] u2 = -α 2 sign(s) (11)
α 1 and α 2 are positive gains. The finite time convergence is guaranteed by the following conditions:

   α 1 ≥ 4C 0 (b max α 2 +C 0 ) b 2 min (b min α 2 -C 0 ) α 2 > C 0 b min (12)
The convergence analysis is shown in [START_REF] Utkin | On convergence time and disturbance rejection of super-twisting control[END_REF].

b) AS controller structure:

The common objectives of the active suspensions widely developed in literature are improving the ride comfort and road holding [START_REF] Savaresi | Semi-active suspension control design for vehicles[END_REF]], [START_REF] Yoon | Design of an unified chassis controller for rollover prevention, manoeuvrability and lateral stability[END_REF]] and [START_REF] Akhmetov | Global Chassis Control for active safety of heavy vehicles[END_REF]]. One objective of this paper is to emphasize new achievable enhancements on the global chassis performance through the coordinated integration of the active suspensions. These enhancements concern directly the rollover and the lateral stability. Hence, the other sub-controllers in the GCC structure become less solicited, and consequently, the safe vertical and lateral ranges of the vehicle manipulation can be enlarged 2), ( 3) and (4). A general form of these dynamics can be written as:

v = g v (X) + f v (X)M v + d v (X,t).
(13) Each of these equations has a unique control input M v , that acts only on the corresponding variable v. Thus, similar controllers with particular gains can be developed for all of these dynamics. To control these dynamics, one can choose the super-twisting sliding mode control law known by its robustness to modeling errors and external disturbances. Let v des = {θ des , φ des , z des } be the desired states and vdes = θdes , φdes , żdes be their time derivatives. Then, let:

e v = v -v des , ( 14
) be the error between the actual and desired states. Let:

s v = ėv + λ v e v ,
(15) be the sliding variable, chosen with a relative degree of 1 w.r.t the control input M v (the control input appears in the first time derivative of the sliding variable) to meet the super-twisting constraints. This means that the discontinuous function appears in the second derivative of the sliding variable such that:

sv (s v ,t) = Φ v (s v ,t) + ξ v (s v ,t) Ṁv (t), (16)
where Φ v (s v ,t) and ξ v (s v ,t) are unknown bounded functions satisfying conditions of (10). The sliding mode control input, based on the Super-Twisting algorithm, is given by:

M v (t) = -α v,1 |s v | τ v sign(s v ) -α v,2 t 0 sign(s v )dτ, (17)
where α v,1 and α v,2 are positive gains satisfying conditions of (12), and τ v ∈]0, 0.5].

The super-twisting algorithm guaranties the convergence of s v in a finite time to zero. Once s v = 0, the states v and v exponentially converge to v des and vdes respectively if λ v > 0. The function sign is smoothed by the approximation sign(s v ) =

s v |s v |+ε v , where ε v > 0.
Once the needed control inputs M θ , M φ , and M z are obtained to control θ , φ , and z, there are different ways to generate them by the active suspension forces on the four vehicle corners. For simplicity, one suggests generating each needed control input by doing a geometrical distribution between the four suspensions as given in (18) (see Fig. 3).

U f l = 0.5 l r l f +l r M θ t f -0.5 M φ l f +l r + 0.5 l r l f +l r M z , U f r = -0.5 l r l f +l r M θ t f -0.5 M φ l f +l r + 0.5 l r l f +l r M z , U rl = 0.5 l f l f +l r M θ t r + 0.5 M φ l f +l r + 0.5 l f l f +l r M z , U rr = -0.5 l f l f +l r M θ t r + 0.5 M φ l f +l r + 0.5 l f l f +l r M z . ( 18
)
2019 IFAC AAC Orléans, France, June 23-27, 2019

The objective of ride comfort in literature is to minimize the roll, pitch and heave angles and velocities/accelerations [START_REF] Savaresi | Semi-active suspension control design for vehicles[END_REF]], [START_REF] Yoon | Design of an unified chassis controller for rollover prevention, manoeuvrability and lateral stability[END_REF]] and [START_REF] Akhmetov | Global Chassis Control for active safety of heavy vehicles[END_REF]], thus, v des = vdes = {0, 0, 0}. Now, the AS control task will be extended to consider the objective of rollover avoidance (vertical stability). The rollover phenomenon starts to happen when the vehicle lateral acceleration exceeds a certain value called the maximal safe lateral acceleration developed in [START_REF] Chen | Rollover prevention using active suspension system[END_REF], which depends on the constant vehicle geometry ratio t f /h and the roll angle as expressed in ( 19):

a y sa f e = 0.7 sign(a y )t f -(h -h r )θ h g. ( 19
)
A lateral acceleration a y above a y sa f e risks the vehicle inner wheels to lift off when cornering. To avoid the rollover, the lateral acceleration a y should be maintained below this threshold.

By minimizing the roll angle, the maximal safe lateral acceleration a y sa f e can be elevated, and thus, prevent the rollover. Accordingly, turning the roll angle in the opposite direction (to the inner side of the corner) will shift a y sa f e more towards a higher value. From our point of view, turning the roll angle towards the inner wheels when cornering reassures the driver and gives him the confidence of piloting the vehicle. The choice of the desired roll angle θ des is done as follows:

-For a y = 0 (straight road), the desired roll angle is 0 • .

-For a y = 0.7 t f h g (maximal safe lateral acceleration threshold), the desired roll angle is equal to the maximal achievable roll angle 10 • (vehicle design constraints).

-The map between θ des and a y is supposed to be linear to make a smooth comfortable roll rate of change. Thus, the desired roll angle θ des is given in (20):

θ des = - 10 π 180 0.7 t f h g a y .
(20)

c) AFS controller structure:

Maneuverability or steer-ability means having a linear relation between the steering provided by the driver and the achieved vehicle yaw rate. The objective of the AFS controller is to enhance the steer-ability, thus, converging the real vehicle yaw rate to a desired one linear to the steer angle provided by the driver. The linear relation can be derived from a linear vehicle model called "bicycle model" [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF]] which represents a stable and ideal motion of the vehicle, where the lateral tires forces are supposed to be linear to the tires side slip angles. The bicycle model is given in ( 21):

ψre f βre f =   -µ l f 2 c f +l r 2 c r I z V x µ l r c r -l f c f I z -1 + µ l r c r -l f c f MV x 2 -µ c f +c r MV x   ψre f β re f + µ l f c f I z µ c f MV x δ d , ( 21
)
where δ d is the driver steer angle on the front wheels, ψre f is the ideal reference yaw rate, β re f is the corresponding side slip angle, and V x is the vehicle longitudinal speed. As the lateral stability is related to the lateral acceleration a y , the authors in [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF] propose to maintain a y below a threshold depending on the maximal possible adherence ( 22), by saturating ψre f , as described in ( 23).

a y V x ( ψ + β ) ≤ µ g, (22) ψre f ,max = 0.85µ g/V x .
(23) The objective of the AFS is thus to converge the measured yaw rate ψ whose dynamics is described in (5) to the saturated reference ψre f , to enhance the maneuverability in the framework of the lateral stability. This can be done by adjusting the driver steering angle δ d through the introduction of the corrective term δ c as the AFS control input calculated based on the super-twisting Sliding Mode control theory. δ d and C z are treated as exogenous inputs to the yaw dynamics of (5). Both exogenous inputs are bounded and supposed to be constants at each iteration.The value of δ d is supposed to be measured by a sensor, while the value of C z is taken from the precedent iteration since it is not calculated yet. Let define the sliding variable as follows:

s ψ = e ψ = ψ -ψre f .
(24) The variable s ψ has a relative degree of 1 w.r.t the control input δ c . Thus,

s ψ (s ψ ,C z , δ d ,t) = Φ ψ (s ψ ,C z , δ d ,t) + ξ ψ (s ψ ,C z , δ d ,t) δc (t). (25) Φ ψ (s ψ ,C z , δ d ,t) and ξ ψ (s ψ ,C z , δ d ,t
) are unknown bounded functions satisfying conditions of (10). By the same reasoning used above, the super-twisting control input δ c can be formulated as (26):

δ c = -α ψ,1 s ψ τ ψ sign(s ψ ) -α ψ,2 t 0 sign(s ψ )dτ. (26)
This algorithm guarantees the convergence of s ψ to zero in a finite time, if the gains α ψ,1 and α ψ,2 satisfy the same convergence conditions of ( 12), and τ ψ ∈]0, 0.5]. This control strategy enhances the maneuverability of the vehicle and maintain the lateral acceleration below the lateralskidding threshold µ.g, where µ is the road adherence coefficient and g is the gravity constant as discussed in [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF]. However, the lateral stability also depends on the vehicle side slip angle and its rate of change. Thus, this control strategy enhances without guarantee the lateral stability, especially when these variables are solicited enough to destabilize the vehicle. To resolve the problem, the first intuitive solution is to introduce the control of β and β in the objectives of the AFS controller. However, the yaw torque provided by the steering in the critical range of lateral stability is not enough to stabilize the vehicle since the lateral tires forces will be saturated. Alternatively, the DYC controller using differential rear braking is known to be effective to control β and β , while it has the disadvantages of: decelerating the vehicle, long-term wheels wear, and driver discomfort. Thus, it is recommended to actuate the DYC controller only under critical situations.

d) DYC controller structure:

The objective of the DYC controller is to minimize the side slip angle β and its rate of change β when the vehicle is under critical driving situations by generating an active yaw moment. The physical actuators to create the yaw moment are selected to be the rear electro-mechanical brakes. This choice prevents direct interference with the active steering on the front tires [START_REF] Doumiati | Integrated vehicle dynamics control via coordination of active front steering and rear braking[END_REF]]. In this subsection, the DYC controller will be developed as a decentralized controller, i.e. to control β and β whatever the driving situation is. Later, in the coordination layer, the DYC controller will be activated based on a decision rule. Similar to the case of the AFS, the super-twisting sliding mode control law is adopted to control β and β , while the control input of the DYC is the additive yaw torque C z . δ is treated as the exogenous input, it is available, bounded and supposed constant at the time iteration. Let the sliding variable be:

s β = β + λ β β . ( 27
)
2019 IFAC AAC Orléans, France, June 23-27, 2019

+ - Sliding Mode Controller + + S q q des λ obj λ q d dt e q Monitor Control input ėq Data ( ψ , β , β ,θ ,ϕ , z , V x ...) q Fig. 4. Scheduled controller
The sliding variable has a relative degree of 1 w.r.t the control input C z . By the same reasoning as before, the super-twisting algorithm guarantees the convergence of s β to zero in a finite time. Thus, β and β converge exponentially to zero if λ β > 0.

Finally, the super twisting sliding mode control input C z is given in ( 28) by:

C z = -α β ,1 s β τ β sign(s β ) -α β ,2 t 0 sign(s β )dτ, (28)
where α β ,1 and α β ,2 satisfy conditions of ( 12), and τ β ∈]0, 0.5].

GCC architecture

Based on the above analysis, a decision layer will be developed in this section to coordinate the proposed sub-controllers. The main idea is to promote/attenuate the control objective by multiplying each sliding variable by a scheduled gain {λ ob j } = {λ AFS , λ DYC , λ AS Roll , λ AS Pitch , λ AS Heave } as depicted in Fig. 4. The decision layer monitors all controllers objectives based on monitoring criteria (data) and a set of coordination rules defined in the following, then, it calculates and sends instantly the exact value of λ ob j to attenuate/promote the corresponding objective. Each of λ ob j varies between 0 and 1. As much λ ob j approaches to 1, as the control objective is promoted, vice versa, the control objective is completely attenuated when λ ob j approaches to 0. From a control point of view, the proof of maintaining the total stability of the global system when injecting these scheduled gains is not given is this paper. Further investigations will be done in future works to demonstrate this issue.

AFS and DYC coordination rules:

The criteria by which the lateral stability can be quantified is called "lateral stability index (SI)". SI reflects the orientation of the vehicle w.r.t its speed vector at the CG, and its rate of change. The lateral stability index (SI) used in Chen et al. ( 2016) is expressed in (29) as:

SI = 2.49 β + 9.55β . ( 29
)
For SI ≤ SI (a predefined threshold depending on the vehicle and road parameters), the vehicle is in normal driving situations, else, the vehicle reaches critical driving conditions (the vehicle has to be controlled to come back to the normal driving situation before losing stability). * If the vehicle situation is normal SI ≤ SI, then the AFS controller should be promoted to improve the maneuverability. In this range, the DYC controller is disabled. * If the vehicle is under critical situation SI ≥ SI, then the DYC controller should be promoted to enhance the lateral stability. In this range, the AFS controller has a poor effect to enhance the lateral stability, thus, it may not be actuated. * To ensure a smooth switch between the controllers, the switching condition will be enlarged to a range of SI, such a range is between two thresholds: SI = 0.6 (low threshold) and SI = 0.8 (high threshold). These thresholds are chosen based on The AFS and DYC will be attenuated/promoted smoothly and continuously in this range as seen in Fig. 5. The switching function is a "sigmoid function". The scheduled gains are given in (30) as:

λ DYC = 1 1+e -8 SI-SI (SI- SI+SI 2 )
,

λ AFS = 1 -λ DYC .
(30)

Active suspension (AS) coordination/actuation rules:

The proposed AS controller will participate in the GCC by achieving three main objectives: roll control, pitch control and heave control. To reduce the excessive actuation of the AS (AS relaxation), while maintaining good ride and stability (vertical and lateral) qualities, the following supervision rules will promote/attenuate these objectives:

-Roll control objective: As we believe that turning the roll angle in the opposite direction improves driver comfort, thus, the roll objective can always be oriented to achieve θ = θ des expressed in (20). By this procedure, the ride comfort (in terms of roll motion) and the stability (lateral and vertical) will be enhanced regardless of SI. Thus, λ AS Roll = 1 whatever the vehicle situation is.

-The Pitch control objective has to be attenuated/promoted depending on the severity of braking/acceleration, to reduce the use of the AS while maintaining good ride quality (in terms of pitch motion). Thus, only the harsh and considerable pitch motion has to be minimized, indeed, λ AS Pitch approaches to 1 to promote the pitch control objective. As much the pitch motion becomes soft, as λ AS Pitch will approach more to 0 to attenuate the pitch control objective. One suggests treating λ AS Pitch as a fuzzy-scheduled gain λ AS Pitch which attenuates/promotes the pitch control objective, based on the pitch angle error ( 14) and its rate of change. The pitch angle error and its rate of change are applied to the Fuzzy Logic Controller (FLC) as inputs, and the fuzzy-scheduled gain λ AS Pitch is the output. The reason of choosing the FLC for the decision-making process is due to its simplicity to make the relation between the needed control input and the controlled variables in an intuitive way. and the linguistic rules are usually determined based on an expert knowledge of the system by performing several simulations. Finally, to defuzzify the result/output, the "Mamdani centroid fuzzy inference method" is used [START_REF] Reznik | Fuzzy controllers handbook: how to design them, how they work[END_REF]].

-Heave control objective attenuation/promotion is done in a similar manner to the pitch control objective. That means, a fuzzy-scheduled gain λ AS Heave is obtained to regulate the degree of achievement of the heave control objective depending on the harshness of this motion.

GCC VALIDATION AND SIMULATION

In this section, the proposed GCC system will be validated through two simulation tests (presented later) using Matlab/Simulink. The simulation model of the full vehicle is developed and validated on the professional vehicle simulator "SCANeR Studio" [START_REF] Chokor | Active suspension control to improve passengers comfort and vehicle's stability[END_REF]] and [START_REF] Chen | Rollover prevention using active suspension system[END_REF]].

The first test is a sine steer (Fig. 8) at 100 km/h initial speed. This test solicits the vehicle yaw and lateral motions, as well as the roll motion. The uncontrolled (induced), desired and controlled roll angles are shown in Fig. 9. The lateral Stability Index SI, without controlling the vehicle, increases to reach more than SI = 1 as shown in Fig. 10. That means, the vehicle has lost its lateral stability. The AFS controller alone (dedicated to the maneuverability) could diminish the SI to 1 as shown in the same figure. However, this improvement is not sufficient. The coordinated AFS and DYC controller could maintain the lateral stability under SI = 0.8. This improvement is obtained thanks to 12. In the ranges below the saturation of the yaw rate reference, the uncontrolled vehicle is somehow far away from the yaw rate reference. Meanwhile, all the adopted strategies (AFS, AFS + DYC, and the GCC) converge to the desired yaw rate. This means that the maneuverability is enhanced regardless of the adopted strategy. When the vehicle yaw rate becomes too much high, the control objective attempts to saturate the yaw rate in order to simultaneously enhance the lateral stability and avoid the nonlinear relation between the yaw rate and the driver steering. The AFS is shown to be the most effective controller in making the vehicle yaw rate converges to the desired saturated one. The DYC, by the braking effect to stabilize the vehicle, tends to diminish its kinetic energy, which is reflected by a reduction of the yaw rate. When adding the roll control (by means of AS) to the GCC system to enhance the stability, the DYC controller becomes less solicited, and thus, the yaw rate re-approaches to the desired one.

To evaluate the rollover risk, the Load Transfer Ratio (LTR) used in [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF] and described in (31) is evaluated.

LT R = F z r -F z l F z r + F z l , ( 31
)
where F z r and F z l are the vertical forces on the right and left side wheels respectively. The rollover is supposed to start when the vehicle inner wheels lift off from the ground. Thus, the rollover starts when F z l or F z r becomes zero, which means all the load Figure 13 shows the LTR of the uncontrolled vehicle and the different control strategies. The results show that the LTR is the best when the GCC strategy is adopted compared to other strategies. It can also be noticed that activating the AFS alone has a drawback on the LTR. The fact is because the vertical stability is not considered in the development of the AFS controller. Divers comfort enhancements are noticed when adding the roll control to the GCC system. One observes that:

-The active differential braking on the rear wheels, provided by the DYC controller to stabilize the vehicle, are reduced as shown in Fig. 14. The justification is that the AS contributes to the stabilization process. According to the same figure, the Root Mean Square RMS of the braking torques are reduced by 47% on the rear left wheel and by 36% on the rear right wheel. The RMS reflects the dissipated energy by the braking actuator, which has an impact on its life time. The peak values of both braking are also considerably diminished by 53% and 30% respectively.

-The vehicle speed drop caused by the braking is less reduced as shown in Fig. 15.

-The critical longitudinal slipping of the rear tires caused by the differential braking are limited as shown in Fig. 16. Consequently, the ABS control system (supposed to be integrated into the chassis) will be less solicited. The second test represents a smooth medium accelerating followed by a sharp and hard braking as shown in Fig. 17 As a part of the future work, beside the proof of maintaining the total stability of the system when injecting these scheduled gains, the proposed GCC will be evolved to integrate more interactions, objectives, and sub-controllers. Studies will also focus on the development of a fault tolerant GCC system.

  Fig. 1. Proposed GCC scheme

Fig. 2 .

 2 Fig. 2. Full vehicle model X = [θ , θ , φ , φ , z, ż, z us,i j , żus,ij , ω i j , x, ẋ, y, ẏ, ψ, ψ, β , β ] T . (1)The full model has been validated in[START_REF] Chen | Rollover prevention using active suspension system[END_REF] for the so-called "Family car" vehicle using SCANeR Studio Simulator. Family car is a vehicle in SCANeR Studio Simulator that uses a very accurate vehicle model called Callas vehicle model, where the real dynamics are more detailed. In this section, essentials of the full model are given to show only the dynamics used to develop the GCC controller. These dynamics are given in Equations (2), (3), (4), (5) and (6). To be noted that equations (5) and (6) are linearized w.r.t the control input δ to facilitate their control. However, the GCC approach is validated on the Full vehicle model.θ = g θ (X) + f θ (X)M θ + d θ (X,t), (2) φ = g φ (X) + f φ (X)M φ + d φ (X,t), (3) z = g z (X) + f z (X)M z + d z (X,t), (4) ψ = g ψ (X) + f ψ,δ (X)δ + f ψ,C z (X)C z + d ψ (X,t), (5) β = g β (X) + f β ,δ (X)δ + f β ,C z (X)C z + d β (X,t).(6) M θ , M φ , and M z represent respectively the active roll moment, active pitch moment, and active heave force, as intermediate control inputs. These inputs have to be generated at a lower level control by physical actuators, e.g. Active Suspensions AS forces U i j integrated on four corners. δ = δ d + δ c is the total steering angle at the front wheels, where δ d is the one provided by the driver and δ c is the one provided by the AFS controller. C z is the active yaw torque provided by the DYC controller. C z has to be generated at a lower level control as a differential braking on the rear wheels. g q (X), f v (X), f l,δ (X), and f l,C z (X) where q = {v, l}, v = {θ , φ , z} and l = { ψ, β } are nonlinear continuous functions detailed in Appendix A. d q (X,t) represent modeling errors and external disturbances supposed to be bounded as given in (7).|d q (X,t)| ≤ D q ; q = {θ , φ , z, ψ, β }, (7) where D q are positive constant values. Note:1 -The lateral and longitudinal accelerations used later in the paper are in a fixed reference frame and are noted respectively by a y and a x . In modeling, a y and a x are constructed from ẋ, ẍ, ẏ, ÿ, ψ. V x used later in the paper is the time integral of a x .-In real time control, the controlled variables ψ, φ and θ are measured by gyrometers and provided at the CG of the vehicle. θ and φ are estimated by time integration and could be provided by the Inertial Measurement Unit IMU -if available-. a y , a x and z are measured by accelerometers. ż, z are integrated from z. The side slip angle β and its derivative β could be estimated. Several observer approaches that suit the real time constraints implementation and vehicle dynamics have been proposed in

  , June[23][24][25][26][27] 2019 literature to estimate β and β , e.g. an Extended Kalman Filter EKF based observer as done in[START_REF] Chen | Rollover prevention using active suspension system[END_REF].

Fig. 3 .

 3 Fig. 3. Active forces distribution to more hard maneuvers. Let first develop an AS controller dedicated to ride comfort. The concerned dynamics of ride comfort are the roll, pitch and heave motions of the sprung mass, developed respectively in Equations (2), (3) and (4). A general form of these dynamics can be written as:v = g v (X) + f v (X)M v + d v (X,t).(13) Each of these equations has a unique control input M v , that acts only on the corresponding variable v. Thus, similar controllers with particular gains can be developed for all of these dynamics. To control these dynamics, one can choose the super-twisting sliding mode control law known by its robustness to modeling errors and external disturbances. Let v des = {θ des , φ des , z des } be the desired states and vdes = θdes , φdes , żdes be their time derivatives. Then, let: e v = vv des , (14) be the error between the actual and desired states. Let:

Fig. 5 .

 5 Fig. 5. Switching function of AFS and DYC the simulation results for the used vehicle and road parameters.The AFS and DYC will be attenuated/promoted smoothly and continuously in this range as seen in Fig.5. The switching function is a "sigmoid function". The scheduled gains are given in (30) as:λ DYC =

Fig. 6 .

 6 Fig. 6. Fuzzy sets of the inputs

  Fig. 8. Front wheels steering

Fig. 14 .

 14 Fig. 12. Yaw rate comparison

  . The smooth/sharp acceleration/braking solicits the pitch rate, while the medium/hard value solicits the pitch angle, which are respectively represented by the uncontrolled vehicle in Figs.18a and 18b. The AS controller eliminates the pitch angle and rate motion almost entirely, while the GCC controller only diminishes the high values of the pitch angle and rate to ensure a soft pitch motion. The control inputs of the four AS are depicted in Fig.19. The RMS value of the total input is diminished by 22%.

  Fig. 15. Longitudinal speed

Table 1 .

 1 Nomenclature and vehicle parameters

	Symbols	Description	Parameters values
	CG	Vehicle center of gravity
	I x	Roll moment of inertia of sprung mass	534 [kg.m 2 ]
	I

z Vehicle yaw moment of inertia 1970 [kg.m 2 ] I xz Vehicle yaw-roll product of inertia 743 [kg.m 2 ] h Height of the vehicle CG 0.58 [m] h r Height of the unsprung mass CG 0.31 [m] h θ Sprung mass roll arm 0.27 [m] M s Sprung mass 1126.4 [kg] t f Half front track 0.773 [m] t r Half rear track 0.773 [m] l f Wheelbase to the front 1.0385 [m] l r Wheelbase to the rear 1.6015 [m] µ Road adherence coefficient dry surface= 1 [-] C f ,C r Front, rear tire cornering stiffness 76776 [N/rad] g Gravity constant 9.81 [m/s 2 ] i i = { f : f ront, r : rear} j j = {r : right, l : le f t} t Time [s]

  Five fuzzy sets are defined for each input, and three for the output: {e φ , ėφ } = {NB (Negative Big), NS (Negative Small), ZE (Zero), PS (Positive Small), PB (Positive Big)}; {λ AS Pitch } = {PS, PM (Positive Medium), PB}. The normalized Membership Functions (MFs) of fuzzification of the controller inputs and defuzzification of the controller output are respectively given in Figs. 6a, 6b and 7. To determine the fuzzy controller output λ AS Pitch for the given fuzzy controller inputs e φ and ėφ , the decision matrix of the linguistic control rules is designed and presented in Table2. These fuzzy sets, membership functions,

Table 2 .

 2 Fuzzy rules of

	Degree of membership	0 0.2 0.4 0.6 0.8 1	PS		PM		PB
		0	0.2	0.4		0.6	0.8	1
					λ ASpitch
	Fig. 7. Fuzzy sets of the output
	λ AS Pitch		NB	NS	ėφ ZE	PS	PB
			NB	PB	PB	PM	PM	PS
			NS	PB	PM	PS	PS	PM
	e φ	ZE	PM	PS	PS	PS	PM
			PS	PM	PS	PS	PM	PB
			PB	PS	PM	PM	PB	PB

ACKNOWLEDGEMENTS

The authors would like to thank the Hauts-de-France Region and the European Regional Development Fund (ERDF) 2014/2020 for the funding of this work, through the SYSCOVI project. This work was also carried out in the framework of the Labex MS2T, (Reference ANR-11-IDEX-0004-02) and the Equipex ROBOTEX (Reference ANR-10-EQPX-44-01) which were funded by the French Government, through the program "Investments for the future" managed by the National Agency for Research.

).

(A.10) F i j , F x,i j , and F y,i j are nonlinear functions of X detailed in [START_REF] Rajamani | Vehicle Dynamics and Control[END_REF].