Ronan Guillossou

Julien Le Roux
email: julien.le-roux@u-pec.fr

Angélique Goffin

Romain Mailler

Gilles Varrault

Emmanuelle Vulliet

Catherine Morlay

Fabrice Nauleau

Sabrina Guérin

Vincent Rocher

Johnny Gaspéri
email: johnny.gasperi@ifsttar.fr

Fluorescence excitation/emission matrices as a tool to monitor the removal of organic micropollutants from wastewater effluents by adsorption onto activated carbon Authors

Keywords: Wastewater advanced treatment, Activated carbon, Organic micropollutants, Fluorescence EEM, PARAFAC

Highlights

• Removal of 28 micropollutants and fluorescence EEM indexes was investigated.

• 7 fluorescence EEM indexes specific to adsorption were found using PARAFAC analysis.

• Correlations were found between the removal of spectroscopic indexes and most OMPs.

• UV254 provided much less accurate correlations than most fluorescence indexes.

• OMPs interactions with fluorescing DOM likely promoted their co-adsorption.

found. Lower correlations were also found for the most biodegradable OMPs, which indicated that the occurrence of biological effects could make the monitoring of these compounds more challenging.

Graphical abstract

Abstract

Monitoring the removal of organic micropollutants (OMPs) in advanced wastewater treatment facilities requires expensive and time-consuming analytical methods that cannot be installed online. Spectroscopic techniques such as fluorescence excitation/emission spectroscopy were demonstrated to offer the potential for monitoring OMPs removal in conventional wastewater treatment plants or ozonation pilots but their application to activated carbon (AC) adsorption processes was only investigated at lab scale and not in real treatment facilities. In this study, indexes from fluorescence emission/excitation matrices (EEMs) were used to find correlations with the removal of 28 OMPs from a large-scale AC pilot in fluidized bed employed for wastewater advanced treatment, as well as from batch experiments. Differences in OMPs removal could be observed depending on the operational conditions (i.e. pilot or batch experiments, contact time, type of AC) and the physico-chemical properties of the molecules. 7 PARAFAC components were derived from the fluorescence EEMs of 60 samples obtained before and after adsorption. Positive correlations were obtained between the removal of fluorescence indexes and most OMPs, and correlation coefficients were much higher than the ones obtained with UV254, confirming the interesting potential of fluorescence spectroscopy to accurately monitor adsorption performances at the industrial scale. The highest correlation coefficients were obtained for OMPs having the best removals while the ones that were refractory to adsorption, as well as to interactions with DOM, exhibited weak correlations. These results suggest that interactions between OMPs and fluorescing DOM and their subsequent co-adsorption onto AC were at the origin of the correlations

Introduction

Many organic micropollutants (OMPs), such as household chemicals, personal care products, pesticides or pharmaceuticals are rejected from human activities and are found in raw wastewaters. Some OMPs with specific properties (e.g. biodegradable, hydrophobic or volatile compounds) can be removed during conventional wastewater treatments, but most OMPs are not completely removed by physical and biological treatments and are detected at non-negligible concentrations (i.e. ng/L up to µg/L) after treatment [START_REF] Loos | EU-wide monitoring survey on emerging polar organic contaminants in wastewater treatment plant effluents[END_REF][START_REF] Margot | Treatment of micropollutants in municipal wastewater: Ozone or powdered activated carbon?[END_REF]. The presence of OMPs in wastewater effluents can lead to adverse effects on water bodies and living organisms [START_REF] Luo | A review on the occurrence of micropollutants in the aquatic environment and their fate and removal during wastewater treatment[END_REF]. To deal with this issue, several advanced treatment technologies can be used for the removal of OMPs from wastewater effluents, including oxidation processes [START_REF] Bourgin | Evaluation of a full-scale wastewater treatment plant upgraded with ozonation and biological post-treatments: Abatement of micropollutants, formation of transformation products and oxidation by-products[END_REF], membrane separation [START_REF] Snyder | Role of membranes and activated carbon in the removal of endocrine disruptors and pharmaceuticals[END_REF] and activated carbon (AC) adsorption [START_REF] Benstoem | Performance of granular activated carbon to remove micropollutants from municipal wastewater-A meta-analysis of pilot-and large-scale studies[END_REF][START_REF] Margot | Treatment of micropollutants in municipal wastewater: Ozone or powdered activated carbon?[END_REF].

The efficiency of a given technology is generally assessed by the determination of OMPs removal rates. The average removal of quantified OMPs is a common indicator used to estimate the overall performance of a process towards the removal of micropollutants (e.g. the 80% targeted by the Swiss legislation). OMPs removals are calculated from concentrations before and after treatment that are determined by targeted chemical analysis. Those analyses are time-consuming, require multiple sample preparation steps (large volume sampling, preconcentration, elimination of interfering substances), heavy and expensive equipment for detection steps (e.g. liquid chromatography coupled to mass spectrometry) as well as qualified personnel.

Thus, there is a need for complementary tools such as spectroscopic methods that could be installed online to improve the control of advanced wastewater treatment facilities (i.e. dosage of reagents, exhaustion of a granular AC bed, membrane clogging) by using surrogate models [START_REF] Korshin | Spectroscopic surrogates for real time monitoring of water quality in wastewater treatment and water reuse[END_REF]. UV absorbance and fluorescence spectroscopy are widely used for the study of dissolved organic matter (DOM) in wastewater treatment plants (WWTP) [START_REF] Carstea | Fluorescence spectroscopy for wastewater monitoring: A review[END_REF][START_REF] Goffin | Towards a better control of the wastewater treatment process: excitation-emission matrix fluorescence spectroscopy of dissolved organic matter as a predictive tool of soluble BOD5 in influents of six Parisian wastewater treatment plants[END_REF]. Different methods have been developed to interpret data from fluorescence excitation/emission matrix (EEM) spectroscopy and to track DOM changes, in terms of quality and quantity, in aquatic ecosystems and water treatment facilities [START_REF] Chen | Fluorescence Excitation-Emission Matrix Regional Integration to Quantify Spectra for Dissolved Organic Matter[END_REF][START_REF] Coble | Characterization of marine and terrestrial DOM in seawater using excitation-emission matrix spectroscopy[END_REF][START_REF] Parlanti | Dissolved organic matter fluorescence spectroscopy as a tool to estimate biological activity in a coastal zone submitted to anthropogenic inputs[END_REF]. Efforts have been made to monitor various families of OMPs by using the direct fluorescence signal of organic molecules (e.g., polycyclic aromatic hydrocarbons, pesticides, pharmaceuticals, volatile organic compounds) [START_REF] Carstea | Fluorescence spectroscopy for wastewater monitoring: A review[END_REF][START_REF] Ferretto | Identification and quantification of known polycyclic aromatic hydrocarbons and pesticides in complex mixtures using fluorescence excitation-emission matrices and parallel factor analysis[END_REF] but the high concentrations of bulk DOM in wastewater hinders the direct detection of trace levels of OMPs [START_REF] Wasswa | Assessing the potential of fluorescence spectroscopy to monitor contaminants in source waters and water reuse systems[END_REF]. EEMs can nevertheless be used as surrogates for the prediction of OMPs removal, for example during primary and secondary wastewater treatment [START_REF] Sgroi | Use of fluorescence EEM to monitor the removal of emerging contaminants in full scale wastewater treatment plants[END_REF], because OMPs and DOM undergo common elimination mechanisms. In this context, the removal of specific components related to aromatic proteins and tyrosine-like substances was successfully correlated with the elimination of easily removed OMPs, while another component related to humic-like substances was correlated with some moderately removed OMPs.

Both UV absorbance at 254 nm (UV254) and fluorescence EEM spectroscopy have been used for over ten years as surrogate parameters to monitor OMPs removal during ozonation of wastewater effluents [START_REF] Chys | Surrogate-Based Correlation Models in View of Real-Time Control of Ozonation of Secondary Treated Municipal Wastewater-Model Development and Dynamic Validation[END_REF][START_REF] Gerrity | Development of surrogate correlation models to predict trace organic contaminant oxidation and microbial inactivation during ozonation[END_REF][START_REF] Nanaboina | Evolution of Absorbance Spectra of Ozonated Wastewater and Its Relationship with the Degradation of Trace-Level Organic Species[END_REF][START_REF] Park | Predicting trace organic compound attenuation by ozone oxidation: Development of indicator and surrogate models[END_REF]. Spectroscopic methods were also applied for the monitoring of OMP removals by AC adsorption. Satisfactory linear correlations were obtained between the removal of UV254 and the removal of specific OMPs or the average removal of several OMPs and for different types of AC (powdered -PAC, micro-grain -µGAC and granular activated carbon -GAC) [START_REF] Sgroi | Modeling emerging contaminants breakthrough in packed bed adsorption columns by UV absorbance and fluorescing components of dissolved organic matter[END_REF]Zietzschmann et al., 2014a[START_REF] Zietzschmann | Comparing and modeling organic micro-pollutant adsorption onto powdered activated carbon in different drinking waters and WWTP effluents[END_REF]. Compared to UV254, better correlations were obtained using total fluorescence (TF, calculated as the total volume integrated under an EEM) for the removal of 13 OMPs by GAC filtration using rapid small-scale columns [START_REF] Anumol | Predicting trace organic compound breakthrough in granular activated carbon using fluorescence and UV absorbance as surrogates[END_REF], because of its higher sensitivity and selectivity. [START_REF] Ziska | Predicting trace organic compound attenuation with spectroscopic parameters in powdered activated carbon processes[END_REF] also successfully developed surrogate models for the removal of 14 OMPs with PAC in batch reactors using power functions based on UV254 or TF, again showing better sensitivity of TF. This was attributed to the greater affinity of fluorophores for AC than UV-absorbing matter.

Recently, [START_REF] Sgroi | Modeling emerging contaminants breakthrough in packed bed adsorption columns by UV absorbance and fluorescing components of dissolved organic matter[END_REF] used PARAFAC analysis to study the breakthrough of DOM through GAC rapid small-scale columns. Both UV254 and PARAFAC fluorescence components were successful in predicting the breakthrough of 11 OMPs. A better sensitivity was observed with fluorescence indicators (PARAFAC components) than with UV254. To our knowledge, no study reported the use of fluorescence indexes to predict OMPs removal by AC processes at the industrial scale. Apart from the study of Sgroi et al. (2018), only UV254 and TF were employed in models to predict OMPs behavior and no other EEM data processing methods were used (e.g. fluorescence regional integration, peak-picking or PARAFAC analysis).

Moreover, the physico-chemical mechanisms and potential biological effects underlying the correlations between the removal of OMPs and spectroscopic indexes are not known and are often overlooked in the literature.

The aim of this study was to find correlations between the removal of fluorescence EEM indexes and OMPs from wastewater effluents by adsorption onto AC at the industrial scale and to show that 3D fluorescence is a promising tool for the monitoring of OMPs, especially since online applications of fluorescence spectroscopy are being developed. Data were gathered both from a pilot used for wastewater advanced treatment with µGAC at the industrial scale and from batch experiments using PAC. Experimental conditions covered a range of various conditions to obtain statistically significant variations of OMPs removal. 28 OMPs exhibiting a wide range of physico-chemical properties were targeted based on their occurrence in the wastewater effluent. Correlation coefficients between each OMP and each fluorescence index were explored and discussed by considering the various effects of interactions between DOM and OMPs and their implication on the adsorption processes and the monitoring of OMPs. The occurrence of biological processes in adsorption-based treatments has been reported but their contribution to the elimination of OMPs is difficult to estimate, especially at the industrial scale [START_REF] Piai | Diffusion of hydrophilic organic micropollutants in granular activated carbon with different pore sizes[END_REF][START_REF] Zietzschmann | Fast empirical lab method for performance projections of large-scale powdered activated carbon re-circulation plants[END_REF]. The potential influence of biodegradation on the correlations was thus also investigated. Finally, the perspective of building models for the prediction of OMPs elimination was discussed.

Materials and methods

AC pilot tests

The AC industrial pilot (CarboPlus ® , Saur, Figure S1 in supplementary information) was based on a 1,000 kg bed of micro-grain AC being continuously renewed by equivalent addition (daily) and extraction (weekly) [START_REF] Guillossou | Organic micropollutants in a large wastewater treatment plant: What are the benefits of an advanced treatment by activated carbon adsorption in comparison to conventional treatment?[END_REF]Mailler et al., 2016a). A dose of 10 g of fresh AC per m 3 of wastewater effluent was applied daily, corresponding to 8.6 kg of AC per day for a flow rate of 860 m 3 /day. Once a week, after washing the filter to remove the retained suspended solids, 60 kg of AC was removed from the bed to maintain a constant age and mass of AC over time. This mode of operation ensures that fresh AC is available at all times, thus guaranteeing a high and continuous adsorption efficiency. The bed was fluidized in a 5 m high and 2.39 m² surface reactor with an ascendant fluid velocity of 15 m/h and an average hydraulic retention time of about 20 min. The pilot was continuously fed with denitrified water (sampled after the third biofiltration stage) from the Seine-Centre WWTP (Colombes, France). The plant is operated by the Paris public sanitation service (SIAAP) and treats wastewater for 800,000 inhabitants with a flow of 240,000 m 3 /day. The treatment is composed of a pre-treatment step (screening, grit and oil removal) followed by primary treatment (physico-chemical lamellar settling, removal of suspended particles, colloids and phosphorus) and biological treatment (3 stages of biofiltration, removal of carbon, nitrification and denitrification). 17 sampling campaigns (each consisting of one 24h composite sample from the inlet of the pilot and one from the outlet) were carried out between 2015 and 2019 with the industrial pilot (Table 1). The pilot was successively operated using two μGACs, CycleCarb 305 (Chemviron Carbon) from 2015 to 2017 (sampling campaigns #1-12) and Norit 3040 (Cabot) from 2018 to 2019 (sampling campaigns #13-17). The first 16 sampling campaigns occurred while the AC bed was being continuously renewed (nominal condition) and one last occurred at a time of no renewal for approximately 60 days (renewal of the bed was stopped to study the kinetics of OMPs removal in the absence of fresh AC and to obtain lower values of removal rates from the pilot). For each campaign, the WWTP effluent and the pilot effluent were sampled, consisting in 20 L of 24 h composite samples collected by automatic samplers equipped with Teflon ® pipes in cleaned glass bottles refrigerated at 4 °C. The properties of the AC are available in Table S1 and conventional wastewater quality parameters during each sampling campaigns are provided in Table S2 (supplementary information).

Batch experiments

13 adsorption experiments (experiments #18-30) were carried out using various types of PAC at a dose of 10 mg/L between 2018 and 2019 at the laboratory (i.e. batch tests) (Table 2). PAC was prepared from μGAC crushed and sieved to retain a fraction between 50 and 63 µm in order to ensure fast adsorption kinetics.

Wastewater effluent was sampled from the Seine Centre WWTP at two different stages with a similar quality:

nitrified water before the third biofiltration stage (i.e. denitrification stage) and denitrified water after the third biofiltration stage (i.e. similar to AC pilot tests). 8 different PACs and two contact times (30 min and 72 h) were used for adsorption experiments. For each experiment, samples were collected before and after adsorption in cleaned glass bottles for analyses. The properties of the PAC are available in Table S1 and conventional wastewater quality parameters during each experiment are provided in Table S2 (supplementary information).

Analytical procedures

28 OMPs (20 pharmaceuticals, 5 pesticides, 2 hormones and 1 perfluorinated acid) were analyzed within 48 h at the Institute of Analytical Sciences (ISA -Villeurbanne, France) by liquid chromatography coupled to tandem mass spectroscopy. Prior to analysis, all samples were homogenized and filtered on 0.7 µm GF/F glass filters (Whatman). More information on the analytical methods can be found in the literature [START_REF] Vulliet | Occurrence of pharmaceuticals and hormones in drinking water treated from surface waters[END_REF]. Details about OMPs physico-chemical properties and the analytical procedures are provided in the supporting material (Table S3, supplementary information).

Dissolved organic carbon (DOC) was analyzed for each experiment and sampling campaign by the certified SIAAP laboratory after filtration on 0.45 µm polyvinylidene fluoride filters (Milex ® , Merck) (limit of quantification = 0.3 mgC/L). Spectroscopic measurements were performed at room temperature directly after sampling and filtration on 0.45 µm polyvinylidene fluoride filters (Milex ® , Merck). UV254 was measured using a spectrophotometer (Genesys 10S UV-Vis, Thermo Scientific). EEMs (fluorescence excitation/emission matrix) were obtained using a spectrofluorometer (FP-8300, 150-W Xenon lamp, Jasco)

with the scanning range from excitation wavelength 240 nm to 450 nm at an interval of 5 nm and emission wavelength from 250 nm to 600 nm at an interval of 2 nm. If the UV254 was higher than 0.080 cm -1 , the samples were diluted with ultrapure water to avoid inner filter effects due to adsorbing species present in the wastewater [START_REF] Alberts | Comparison of the natural fluorescence distribution among size fractions of terrestrial fulvic and humic acids and aquatic natural organic matter[END_REF]. Since UV254 of wastewater effluents was always < 0.15 cm -1 , low dilution factors (< 2) were used to minimize sources of errors [START_REF] Kothawala | Inner filter correction of dissolved organic matter fluorescence: Correction of inner filter effects[END_REF]. EEMs of ultrapure water were subtracted from the sample EEMs and normalized by the Raman peak of ultrapure water at an excitation wavelength of 350 nm to obtain fluorescence data in Raman units (R.U.), and fluorescence intensities were corrected with dilution factors when needed [START_REF] Lawaetz | Fluorescence Intensity Calibration Using the Raman Scatter Peak of Water[END_REF].

Fluorescence data treatment

Three methods were used to process fluorescence data (Table S4). All of them were performed using a peakpicking approach, which consists of extracting fluorescence intensities measured at specific pairs of Ex/Em (excitation/emission) wavelengths from measured EEMs. The first extraction method used Ex/Em wavelengths defined by [START_REF] Parlanti | Dissolved organic matter fluorescence spectroscopy as a tool to estimate biological activity in a coastal zone submitted to anthropogenic inputs[END_REF] (α, α' and β indexes related to humic-like components, γ and δ indexes related to protein-like components) as they are frequently used in the literature for a large range of aquatic environments. A second peak-picking approach was chosen based on Ex/Em maximum localization of 6 PARAFAC components (C1-C3 related to protein-like components and C4-C6 related to humic-like components) previously obtained with raw wastewater from the same WWTP than the one studied in this work [START_REF] Goffin | Towards a better control of the wastewater treatment process: excitation-emission matrix fluorescence spectroscopy of dissolved organic matter as a predictive tool of soluble BOD5 in influents of six Parisian wastewater treatment plants[END_REF]). Finally, a set of Ex/Em wavelengths was based on Ex/Em maximum localization of 7 PARAFAC components (F1-F7) obtained in this study. The PARAFAC analysis was performed using MATLAB ® with the DrEEM toolbox [START_REF] Murphy | Fluorescence spectroscopy and multi-way techniques[END_REF] from 30 WWTP effluent samples before and after adsorption onto AC (n = 60). Further details on the procedure used for PARAFAC analysis are presented in [START_REF] Goffin | Towards a better control of the wastewater treatment process: excitation-emission matrix fluorescence spectroscopy of dissolved organic matter as a predictive tool of soluble BOD5 in influents of six Parisian wastewater treatment plants[END_REF]. EEMs contours plots and Ex/Em loadings of the seven fluorescent components identified in this study are presented in Figure S2.

Data processing

OMPs removal was calculated following the approach of [START_REF] Choubert | Rethinking micropollutant removal assessment methods for wastewater treatment plantshow to get more robust data?[END_REF], which stated that the uncertainty of OMP concentrations in wastewater generally ranges between 30% and 100% when the measured value is lower than 2.5 to 10 times the limit of quantification (LOQ) of the compound. Therefore, when a compound was quantified at levels above 5 times the LOQ in the WWTP effluent and above the LOQ in the pilot effluent, the removal was conventionally calculated. When a compound concentration was above 5 times the LOQ in the WWTP effluent but below the LOQ in the pilot effluent, the removal was estimated using LOQ/2. Removals were not calculated when concentrations in both the WWTP and the pilot effluent ranged between the LOQ and 5 times the LOQ.

The relationships between the removal of OMPs and spectroscopic indexes was examined using the R software [START_REF] Core | R: A language and environment for statistical computing[END_REF]. Pearson correlations with a p-value higher than 0.05 were discarded to ensure that results were statistically significant.

Results and discussion

OMPs removal

Out of the 28 OMPs analyzed, 7 molecules (ciprofloxacin, clothianidin, imidacloprid, estrone, estradiol, thiacloprid and thiamethoxam) were detected less than 10 times among the 30 wastewater effluent samples analyzed before adsorption. The results for these molecules were therefore not presented to only retain statistically significant results. Concentrations of OMPs in the wastewater effluent typically ranged from ng/L levels up to several µg/L (e.g., acetaminophen or sulfamethoxazole) at the time of each sampling campaign or batch experiment (Table S5, supplementary information). The removal of the 21 OMPs selected and the average removal for each experiment/sampling campaigns (17 sampling campaigns on the pilot and 13 batch experiments) are presented in Table 3. Various removals were observed depending on the experimental conditions (i.e. pilot-scale or batch experiments, contact time and type of AC used) and the affinity of OMPs toward AC (Figure S3-S6). The average removals obtained from the industrial pilot (61% in average, sampling campaigns #1-16) were higher than those obtained at lab-scale (30% in average, experiments #18-28) for a close contact time (20 min and 30 min, respectively). The performances observed in the pilot were higher due to the large mass of AC permanently present in the bed (1,000 kg) and the amount of available adsorption site, similarly to a GAC filter. Most importantly, the dose of fresh AC added daily (8.7 kg) was previously demonstrated to be the major parameter controlling the adsorption efficiency (40% removals at a 5 mg/L dose and up to >95% at a 70 mg/L dose) (Mailler et al., 2016b[START_REF] Mailler | Study of a large scale powdered activated carbon pilot: Removals of a wide range of emerging and priority micropollutants from wastewater treatment plant effluents[END_REF]. When the AC bed was not renewed for 2 months (sampling campaign #17), a decrease in adsorption performance was thus observed (from 61% to 35%) due to the absence of fresh AC and the progressive saturation of the adsorption sites. At lab-scale, the average removal increased from 30% to 79% when the contact time increased from 30 min (experiments 18-28) to 72 h (experiments 29 and 30). It is well known that when the contact time increases, the molecules can diffuse from the liquid phase and adsorb onto the AC more easily [START_REF] Moreno-Castilla | Adsorption of organic molecules from aqueous solutions on carbon materials[END_REF]. The presence of DOM hinders the diffusion of OMPs into the AC porosity, which therefore need more time to adsorb [START_REF] Newcombe | Simultaneous adsorption of MIB and NOM onto activated carbon II[END_REF]. 5 OMPs (acetamiprid, diuron, norfloxacin, propranolol and trimethoprim) were better eliminated than the others, both in the industrial pilot and in laboratory (Figure S3, supplementary information). Among these OMPs, some have physico-chemical properties that may promote their adsorption, such as a small molecular size (acetamiprid and diuron) or a positive charge (norfloxacin, propranolol and trimethoprim) in WWTP effluent [START_REF] Alves | Influencing factors on the removal of pharmaceuticals from water with micro-grain activated carbon[END_REF][START_REF] Margot | Treatment of micropollutants in municipal wastewater: Ozone or powdered activated carbon?[END_REF]. On the contrary, 5 OMPs (erythromycin, PFOS, roxithromycin, sulfadiazine and sulfamethoxazole) were less eliminated than the others (Figure S4, supplementary information). Erythromycin and roxithromycin are large molecules and thus could be subjected to steric hindrance when they diffuse to adsorption sites and could compete with DOM for adsorption sites in large micropores and mesopores. Sulfadiazine and sulfamethoxazole are negatively charged and thus can be subjected to repulsive electrostatic interactions with the adsorbed DOM (also negatively charged). PFOS is also a large and negatively charged molecule exhibiting a low removal, despite the presence of a long hydrophobic chain which should allow hydrophobic interactions with the surface of the AC. 6 OMPs (atenolol, carbamazepine, diclofenac, naproxen, ofloxacin and oxazepam) had a removal close to the average removal of all OMPs (Figure S5, supplementary information). Interestingly, several OMPs (acetaminophen, ibuprofen, lorazepam and sulfadiazine) clearly exhibited higher removals in the pilot (in optimal conditions) than in batch experiments after 72h of contact time (Table 3, Figure S6). Since some biological activity has been indirectly observed in the industrial pilot through the occurrence of nitratation [START_REF] Guillossou | Organic micropollutants in a large wastewater treatment plant: What are the benefits of an advanced treatment by activated carbon adsorption in comparison to conventional treatment?[END_REF]Mailler et al., 2016a), this could be due to the occurrence of biodegradation in the AC bed of the industrial pilot. Although it is recognized that degradation/biosorption by biomass processes (e.g. biological activated carbon filters, sand filters, fixed bed, moving bed) have a limited efficiency regarding the removal of most OMPs (<16%) [START_REF] Bourgin | Evaluation of a full-scale wastewater treatment plant upgraded with ozonation and biological post-treatments: Abatement of micropollutants, formation of transformation products and oxidation by-products[END_REF][START_REF] Falås | Tracing the limits of organic micropollutant removal in biological wastewater treatment[END_REF], biodegradation could still be significant for the most biodegradable compounds. Except lorazepam, these molecules (i.e.

acetaminophen, ibuprofen and sulfadiazine) were indeed demonstrated to be highly removed by conventional WWTP (>78%) and thus to be easily amenable to biodegradation [START_REF] Ben | Occurrence, removal and risk of organic micropollutants in wastewater treatment plants across China: Comparison of wastewater treatment processes[END_REF][START_REF] Guillossou | Organic micropollutants in a large wastewater treatment plant: What are the benefits of an advanced treatment by activated carbon adsorption in comparison to conventional treatment?[END_REF][START_REF] Verlicchi | Occurrence of pharmaceutical compounds in urban wastewater: Removal, mass load and environmental risk after a secondary treatment-A review[END_REF]. Other easily biodegradable compounds (e.g., naproxen, erythromycin) did not follow the same behavior and were less eliminated in the pilot than after 72h in batch experiments. Other elimination processes (e.g. different adsorption kinetics, interactions with DOM or other components of wastewater effluents) might thus compensate the effect of biodegradation.

More detailed information on the performances of the AC pilot and the influence of OMPs physico-chemical properties on their adsorption can be found in previous studies [START_REF] Guillossou | Organic micropollutants in a large wastewater treatment plant: What are the benefits of an advanced treatment by activated carbon adsorption in comparison to conventional treatment?[END_REF](Guillossou et al., , 2020a;;Mailler et al., 2016a).

Spectroscopic indexes removal

7 components were obtained from fluorescence EEMs (n = 60) using PARAFAC analysis (Figure S2). S4, SI) [START_REF] Chen | Fluorescence Excitation-Emission Matrix Regional Integration to Quantify Spectra for Dissolved Organic Matter[END_REF].

F7 exhibited a second peak of lower intensity (Ex/Em 270/472 nm), also related to fulvic-like compounds.

A significant loss of intensity was observed in all regions of EEMs after adsorption, illustrating the efficiency of AC in removing fluorescing DOM (Figure S7, supplementary information). The removal of DOC, UV254 and all fluorescence indexes was, like the removal of OMPs, higher in the industrial pilot in nominal configuration and at lab-scale for a longer contact time (Table 4). Apart from the F1 index, close to the background noise of fluorescence EEMs, the removal of UV254 and DOC was most of the time lower than those of fluorescence indexes, indicating that fluorescing moieties of DOM were preferentially eliminated. Similar trends in the removal of fluorescence indexes were observed both in the industrial pilot and at lab scale. Slightly higher removals were obtained for tryptophan-like (F2) and tyrosine-like (F3) indexes (Table 4). Other organic compounds (i.e. humic-like and fulvic-like material, F4-F7) were slightly less removed, especially at lab-scale after 30 min. Similar results were obtained with indexes derived from other studies [START_REF] Goffin | Towards a better control of the wastewater treatment process: excitation-emission matrix fluorescence spectroscopy of dissolved organic matter as a predictive tool of soluble BOD5 in influents of six Parisian wastewater treatment plants[END_REF][START_REF] Parlanti | Dissolved organic matter fluorescence spectroscopy as a tool to estimate biological activity in a coastal zone submitted to anthropogenic inputs[END_REF] (Table S6).

Humic-like indexes (F4-F7) were more affected by the absence of AC renewal (and thus saturation of the adsorption sites) than protein-like indexes (F1-F3). For example, the reduction of the F5 index went from 36% (sampling campaigns #1-16) to 16% (sampling campaigns #17) while the F2 index only decreased from 40% to 35%. These results could indicate that protein-like components are less sensitive to adsorption phenomena, but also that they could be more easily biodegraded. However, these results would need to be confirmed with more data in the absence of fresh AC.

Correlations between OMPs removal and spectroscopic indexes

A regression analysis was performed to examine relationships between the removal of OMPs and spectroscopic indexes. Correlation coefficients (rPearson) from the statistically significant regressions (p-value < 0.05) are reported in Table 5. Positive correlations were obtained between the removal of spectroscopic indexes and all OMPs, indicating that an increase in the elimination of fluorescing DOM (i.e. represented by the elimination of the indexes) did not hinder the elimination of OMPs (e.g. through competitive mechanisms). The adsorption of fluorescing DOM thus did not block all micropores where OMPs are preferentially adsorbed [START_REF] Li | Effects of activated carbon surface chemistry and pore structure on the adsorption of organic contaminants from aqueous solution[END_REF]. These positive correlations also suggested that OMPs and DOM, despite different physicochemical properties (e.g. molecular weight or electric charge), followed similar adsorption kinetics and mechanisms and/or that they interacted and were adsorbed together. The formation of DOM-OMPs complexes in the dissolved phase and their subsequent adsorption on PAC was indeed reported in similar conditions (Guillossou et al., 2020b). In complex wastewater matrix, interactions between OMPs and extracellular polymeric substances (EPS) have also been reported through adsorption by the proteinaceous components of EPS or some binding with metal ions [START_REF] Yu | Molecular Insights into Extracellular Polymeric Substances in Activated Sludge[END_REF][START_REF] Zhang | Understanding the Role of Extracellular Polymeric Substances on Ciprofloxacin Adsorption in Aerobic Sludge, Anaerobic Sludge, and Sulfate-Reducing Bacteria Sludge Systems[END_REF]. This could also play a role in the common adsorption observed between OMPs and fluorescence indexes, since the soluble EPS fraction show fluorescence signals in both protein-like and humic-like regions [START_REF] Ni | Characterization of extracellular polymeric substances produced by mixed microorganisms in activated sludge with gelpermeating chromatography, excitation-emission matrix fluorescence spectroscopy measurement and kinetic modeling[END_REF][START_REF] Sheng | Characterization of extracellular polymeric substances of aerobic and anaerobic sludge using three-dimensional excitation and emission matrix fluorescence spectroscopy[END_REF]. All the studied indexes provided statistically significant correlations with most OMPs (i.e. p-values < 0.05), despite the use of different brands of AC and various grain sizes, which suggests that these results could be transposed to other activated carbons. The correlation coefficients between the removal of OMPs and TF, frequently used in OMPs adsorption studies, were similar to results obtained with other indexes (especially F4 and F5). Despite being less specific than indexes derived from peak-peaking, TF is a promising spectroscopic index to be used in future prediction models of OMPs removal. Interestingly, there were no significant differences between the correlation coefficients obtained with the indexes obtained by PARAFAC analysis and other indexes from the literature [START_REF] Goffin | Towards a better control of the wastewater treatment process: excitation-emission matrix fluorescence spectroscopy of dissolved organic matter as a predictive tool of soluble BOD5 in influents of six Parisian wastewater treatment plants[END_REF][START_REF] Parlanti | Dissolved organic matter fluorescence spectroscopy as a tool to estimate biological activity in a coastal zone submitted to anthropogenic inputs[END_REF] (Table S7), because of the proximity of their Ex/Em wavelengths. This indicates that the development of specific EEMs indexes does not appear essential to improve the correlation results in the case of adsorption studies. However, the removal of DOC and more importantly of UV254 (the most used spectroscopic index in OMPs adsorption studies), were much less correlated with OMPs removal than most fluorescence indexes. Fluorescence spectroscopy thus offers the advantage of being more specific to several fractions of DOM with various chemical structures as compared to UV254, which is mostly related to DOM aromaticity [START_REF] Leenheer | Characterizing Aquatic Dissolved Organic Matter[END_REF]. Fluorescence EEMs thus take into account numerous DOM fractions that interact with OMPs, or that follow similar adsorption mechanisms despite their different molecular properties.

Strong correlations (rPearson > 0.90) were obtained between the removal of TF and fluorescence indexes related to humic and fulvic-like compounds (F4, F5, F6 and F7) and the removal of 6 OMPs (acetamiprid, atenolol, diuron, ofloxacine, propranolol and trimethoprim) (Figure S8). The average removal was also best correlated (rpearson = 0.92) with humic-like fluorescence indexes from recent biological activity (F4, F5) (Figure 1).

Moderate correlations (rPearson > 0.80) were also obtained between these indexes and the removal of carbamazepine, diclofenac, ibuprofen, ketoprofen, naproxen, norfloxacin and oxazepam (Figure 1, Figure S8). The best correlations for acetaminophen and tetracycline were obtained with the indexes related to tyrosine-like compound (γ and F2), while the highest correlation coefficient for PFOS was obtained with UV254 (rPearson = 0.73). Weaker correlations (rPearson < 0.80) were found for erythromycin, lorazepam, roxithromycin, sulfadiazine or sulfamethoxazole with any index. Interestingly, the most biodegradable OMPs (acetaminophen, ibuprofen, lorazepam and sulfadiazine) which exhibited higher removals in the pilot than in batch experiments also showed low correlation coefficients with spectroscopic indexes (rPearson < 0.82) (Table 5), which confirms that other processes than adsorption influenced their elimination. Monitoring these specific OMPs might thus prove more challenging. The occurrence of biodegradation might also explain the lower correlation coefficients globally obtained with protein-like indexes. Overall, even if some biodegradation could be expected for the most biodegradable compounds, robust correlations were obtained between the average removal and humic-like indexes, which indicated that biological effects had a low influence on the whole pool of OMPs. High correlation coefficients obtained with several OMPs (e.g., atenolol, trimethoprim) also suggested that these specific molecules were mostly eliminated by adsorption processes.

Interactions between OMPs, fluorescing DOM and AC

There was no apparent link between a specific physico-chemical property of OMPs and the indexes with which they were correlated. Complex interactions (e.g. electrostatic, hydrophobic and van der Walls) exist between AC, OMPs and DOM, and a single property cannot account for all these phenomena. For example, the removal of both atenolol and ofloxacin was well correlated (rPearson >0.90) with the removal of the F4 component (humic-like from recent biological activity), but atenolol is positively charged while ofloxacin is negatively charged in wastewater effluents. As mentioned earlier, the correlations observed between OMPs and fluorescing DOM could be due to similar adsorption kinetics and mechanisms and/or to DOM-OMPs and DOM can be first considered since it is known that smaller fractions of DOM can compete with OMPs for adsorption sites [START_REF] Newcombe | Simultaneous adsorption of MIB and NOM onto activated carbon II[END_REF]Zietzschmann et al., 2014b). Such competition was associated with higher proportions of small acid and neutral compounds of DOM and was assumed to result from the similar molecular size range of these DOM compounds and most OMPs, which in turn targeted similar adsorption sites (Zietzschmann et al., 2014b). It is however uncertain if such competition would lead to correlations between the removals of DOM and OMPs, especially when considering their respective concentrations (i.e. mg/L levels of DOM compounds and ng/L-µg/L levels of OMPs). Moreover, OMPs with different molecular properties and different adsorption behaviors were affected differently by these competition effects (Zietzschmann et al., 2014b). In our study, it is also not possible to infer that the obtained correlations were due to common molecular sizes since fluorophores cannot be associated with specific ranges of molecular size. Additional experiments would thus be needed to evaluate the relevance of competition effects with small fractions of DOM to the adsorption of OMPs presented in this study.

The occurrence of interactions between fluorescing DOM or EPS and OMPs could also explain the observed correlations. Such interactions (e.g. hydrogen bonding, hydrophobic, van der Waals or dipole-dipole interactions) were demonstrated between various OMPs and several types and fractions of natural DOM [START_REF] Caupos | Partitioning of the pesticide trifluralin between dissolved organic matter and water using automated SPME-GC/MS[END_REF][START_REF] Mott | Association of hydrophobic organic contaminants with soluble organic matter: evaluation of the database of Kdoc values[END_REF][START_REF] Yamamoto | Effects of Physical-Chemical Characteristics on the Sorption of Selected Endocrine Disruptors by Dissolved Organic Matter Surrogates[END_REF], effluent DOM (Guillossou et al., 2020b;[START_REF] Ilani | Interactions of Organic Compounds with Wastewater Dissolved Organic Matter: Role of Hydrophobic Fractions[END_REF] and EPS [START_REF] Yu | Molecular Insights into Extracellular Polymeric Substances in Activated Sludge[END_REF][START_REF] Zhang | Understanding the Role of Extracellular Polymeric Substances on Ciprofloxacin Adsorption in Aerobic Sludge, Anaerobic Sludge, and Sulfate-Reducing Bacteria Sludge Systems[END_REF]. [START_REF] Hernandez-Ruiz | Quantifying PPCP interaction with dissolved organic matter in aqueous solution: Combined use of fluorescence quenching and tandem mass spectrometry[END_REF] used fluorescence quenching to examine whether some OMPs could interact with fluorescent moieties of DOM and found that bisphenol-A interacted with microbial byproduct-like and humic acid-like fluorophores while carbamazepine and ibuprofen interacted with fulvic acid-like fluorophores. The impact of these DOM-OMPs associations on the adsorption processes and the occurrence of co-adsorption was recently observed for ciprofloxacin and humic acid adsorption onto AC and various resins [START_REF] Jin | Ultrahigh selective adsorption of zwitterionic PPCPs both in the absence and presence of humic acid: Performance and mechanism[END_REF], as well as for effluent DOM and various OMPs adsorption on AC (Guillossou et al., 2020b). This DOM-OMPs co-adsorption hypothesis is reinforced by the fact that the best correlations were obtained for the OMPs reaching the highest removals (e.g. diuron and propranolol), while the OMPs that were more refractory to adsorption exhibited weaker correlations (e.g.

Toward a prediction of OMPs removal?

Fluorescence spectroscopy appears as an effective tool for the online monitoring of the average removal of OMPs during adsorption processes, which could facilitate the supervision of advanced wastewater treatment facilities. The large variety of physico-chemical properties of selected OMPs suggests that fluorescence spectroscopy could be used to predict the removal of other OMPs found in wastewater, notably the 12 compounds suggested as indicator substances for wastewater treatment in Switzerland (Office fédéral de l'environnement, Division Eaux, 2014). Fluorescence spectroscopy appeared much more accurate than UV254

for the prediction of OMPs removal. While UV254 is currently the only spectroscopic option for high-frequency monitoring, the online measurement of fluorescence is currently under development and would provide more information and accuracy for the monitoring of OMPs adsorption. Considering the lower correlations obtained with highly biodegradable compounds or with OMPs refractory to adsorption, it is worth noting that such application appears more accurate with the average concentration of OMPs and that monitoring specific OMPs could be more challenging.

Robust model development for accurate high-frequency monitoring would require a larger number of samples to allow training and validation of regression models [START_REF] Chys | Surrogate-Based Correlation Models in View of Real-Time Control of Ozonation of Secondary Treated Municipal Wastewater-Model Development and Dynamic Validation[END_REF]. In addition to simple linear regression models, a large dataset would allow to study multiple linear regression models combining different spectroscopic indexes to predict OMPs removal. These models could have greater predictive power than simple models as suggested by several studies [START_REF] Carstea | Fluorescence spectroscopy for wastewater monitoring: A review[END_REF][START_REF] Goffin | An environmentally friendly surrogate method for measuring the soluble chemical oxygen demand in wastewater: use of three-dimensional excitation and emission matrix fluorescence spectroscopy in wastewater treatment monitoring[END_REF][START_REF] Henderson | Fluorescence as a potential monitoring tool for recycled water systems: A review[END_REF]. The combination of different indexes related to different fractions of DOM could account for the possible interactions between OMPs and DOM more accurately, and thus improve the prediction of their removal. The adsorption-specific fluorescence indexes (i.e. specific PARAFAC components) found in this study may also be more accurate than generic indexes for this type of models.

Conclusion

• Out of 28 targeted OMPs, 21 were detected in wastewater over a significant number of sampling campaigns (n >10). Differences in OMPs removal in an industrial pilot and in batch experiments were observed depending on the operational conditions (i.e. pilot or batch experiments, contact time, type of AC) and the physico-chemical properties of the molecules to be eliminated.

• Robust positive correlations were obtained between the removal of spectroscopic indexes obtained by PARAFAC analysis and most OMPs. This indicates that these correlations show the potential of being used to monitor the removal of OMPs in a wide range of operational conditions. Overall, the average removal of all OMPs was well correlated (rpearson = 0.92) with humic-like fluorescing DOM, and correlations were much more accurate than with UV254.

• These positive correlations suggested that OMPs and DOM followed similar adsorption mechanisms or more likely that they interacted and were adsorbed together. However, there was no apparent link between a specific OMPs physico-chemical property and the indexes with which they were correlated. The most biodegradable OMPs and OMPs refractory to adsorption exhibited lower correlations, so their monitoring in full-scale adsorption processes might be more challenging, especially in the presence of biomass.

• An even higher number of samples in the dataset, especially originating from data acquired in even more various experimental conditions, would confirm the observed trends and could be used to build robust regression models by performing cross-validation. This study is nonetheless demonstrating that the application of fluorescence spectroscopy to the monitoring of adsorption processes at the industrial scale can accurately track the evolution of OMPs.

Fig. 1 .

 1 Fig. 1. Statistically significant correlations between the removal of selected OMPs and fluorescence EEM indexes obtained by PARAFAC analysis.

  -adsorption. The hypothesis of similar adsorption mechanisms and kinetics of both OMPs

  roxithromycin and sulfadiazine) (Figure2). The latter OMPs indeed have physico-chemical properties that are unfavorable to interactions with DOM (i.e. a negative charge for sulfadiazine and sulfamethoxazole) or to diffusion through AC porosity (i.e. a large size erythromycin and roxithromycin) due to the presence of DOM. Their lower interactions with DOM or the competition with DOM during adsorption (i.e. adsorption of DOM favored over adsorption of the OMP) can thus explain the weaker correlations. This result indicates that fluorescence EEM could be a suitable tool for the online monitoring of OMPs that are more easily removed by adsorption on AC, but not for OMPs that are more refractory to adsorption.

Fig. 2 .

 2 Fig. 2. Best correlation coefficient (rPearson) obtained between a fluorescence index and an OMP removal compared to the average removal of each OMP for all the experiments performed (industrial pilot + laboratory).

Table 1 .

 1 Details about sampling campaigns performed on the AC industrial pilot, type of μGAC used, and operating conditions.

	Sampling campaign	Year	Period	Activated carbon used	Producer	Operating conditions
	1-2	2015	February
	3-7	2016 September -December	CycleCarb 305	Chemviron	Equivalent extraction and injection
	8-12	2017 September -December

Table 2

 2

	Experiment #	Date	Wastewater quality	PAC	Producer	Contact time with wastewater	Reference for PAC properties
	18			CycleCarb 305*	Chemviron
	19			PC 100 300*	DaCarb
	20			AquaSorb 2000*	Jacobi
	21	19/03/19		AquaSorb 630*	Jacobi
	22		Nitrified water	ReSorb MC*	Jacobi	30 min	(Guillossou et al., 2020a)
	23			Norit GAC 2442*	Cabot
	24			Norit REACT 2442*	Cabot
	25	02/07/18		CycleCarb 305*	Chemviron
	26	07/08/19		CycleCarb 305*	Chemviron
	27					30 min
	28 29	05/08/19	Denitrified wastewater	PB 170	DaCarb	30 min 72 h	(Mailler et al., 2016c)
	30					72 h

. Details about batch experiments performed at the laboratory, type of PAC used, and operating conditions. *μGAC was crushed to PAC before adsorption to ensure fast adsorption kinetics. The retained fraction ranged from 50 to 63 μm.

Table 3 .

 3 Experimental conditions, removal (%) of each OMP and the average removal for each experiment/sampling campaign.

	Experiment /Sampling campaign	Experimental conditions	ACN ACD ATE CAR DIC DIU ERY IBU KET LOR NAP NOR OFL OXA PFOS PRO ROX SDZ SMZ TET TRI Average
	1					40			16		14	99			58	51		68			0	42
	2					46	55	98	27		51	95			73	36		77	62		18	39
	3		57	63	79	53	46	93	48		36	24	12	95	74	47	21	96	22	39	33	99	88
	4		74	60	78	51	50	98	28		64	44	46	81	65	49	9	90	32	33	21	98	86
	5			72	66	38	37	98	25		67	45	47	85	57	40	0	83	16	36	16	22	79
	6		37	61	66	46	42	95	29		64	38	52		63	48	39	86	0	43	34	50	80
	7 8 9 10	Pilot -Nominal condition	0 89 94 79	57 99 99 99	70 85 84 72	38 75 76 59	45 63 66 55	95 99 98 93	27 38 55 31	99 99 98	71 67 71 69	37 69 72 44	51 73 75 58	95 93 91	56 83 79 67	38 71 71 52	33 64 51 36	84 97 96 93	0 52 57 17	35 50 53 39	6 41 62 37	34 88	84 89 93 85
	11		86	99	63	50	38	87	20	99	49	22	53		62	33	43	85	30	52	4		76
	12		77	99	63	55	34	83	33		73	40	53	92	65	43	32	86	13	40	27		80
	13		99		92	84	60	97	33	70	85	72	78	77	84	74	30	99	34	92	56		96
	14		99		94	84	63	96	38	70	93	63	81	72	79	70	57	99	16		61		93
	15		99		83	71	53	98	18		81	98	67	94	70	62	55	93	18	96	51	68	98
	16		99		84	73	50		53	93	72	98	46	95	71	53	50	92	20	96	53	68	90
	17	Pilot -No renewal	99		51	24	17	65	6		75	6	33	0	25	0		54	0		22	32	78
	18		21		26	25	25	43	27		20	16	30		39	24	23	36	27	17	27		30
	19		24		24	23	20	32	19		20	24	23		7	22	28	30	23	13	22		19
	20		25		28	23	21	35	16		11	8	31		23	11	37	35	5	23	15		25
	21		41		43	38	33	64	27		25	23	39		42	28	31	58	11	0	33		45
	22 23 24	Laboratory -30 min	30 50 42		35 31 41	43 25 37	36 17 35	70 45 61	30 10 15		38 12 25	35 0 26	42 23 33		42 33 40	45 18 28	30 37 36	66 48 62	20 6 14	2 30 31	19 22 17		54 35 46
	25				42	38	18		17		29	16	35		37	35	18	67	33		17
	26		33	35	46	42	46	66	33	34	7	32	35	31	47	36	19	80	24	18	20	1	51
	27		9	25	34	41	11	61	20	4	0	2	3		47	23	0	67	0	6	25		45
	28		35	58	49	48	38	60	35	17	28	40	48		55	41	25	75	22	19	26		59
	29	Laboratory -	89	86	91	93	77	98	79	36	70	59	93		98	86	84	99	68	16	42		96
	30	72 h	90	83	92	95	80	98	83	64	80	68	99		98	88	68	99	76	52	43		98

Table 4 .

 4 Removal (% ± standard deviation) of DOC, UV254 and fluorescence indexes in the industrial pilot and at lab-

	scale.
	Index	Pilot -Nominal configuration (experiments #1-16)	Pilot -No renewal (experiment #17)	Laboratory -30 min (experiments #18-28)	Laboratory -72 h (experiments #29-30)
	DOC	21 (± 7)	15	12 (± 6)	27 / 32
	UV254	23 (± 6)	8	12 (± 3)	28 / 29
	TF	38 (± 5)	20	12 (± 7)	48 / 50
	F1	13 (± 48)	0	-24 (± 67)	83 / 84
	F2	40 (± 6)	35	20 (± 11)	48 / 50
	F3	44 (± 6)	31	22 (± 11)	47 / 50
	F4	38 (± 6)	22	10 (± 7)	42 / 43
	F5	36 (± 5)	16	10 (± 8)	46 / 47
	F6	37 (± 7)	21	13 (± 7)	48 / 49
	F7	40 (± 5)	20	6 (± 10)	50 / 52

Table 5 .

 5 Correlation coefficient (rPearson,) values for the linear regressions between the removal of DOC, UV254, fluorescence indexes and the removal of OMPs. The highest value for each OMP is written in bold type. TF = Total Fluorescence. n = number of data for each OMP.

	Index

ACN: Acetaminophen; ACD: Acetamiprid; ATE: Atenolol; CAR: Carbamazepine; DIC: Diclofenac; DIU: Diuron; ERY: Erythromycin; IBU: Ibuprofen; KET: Ketoprofen; LOR:

Tetracycline; TRI: Trimethoprim.241

Acknowledgments

This study was performed within the framework of the OPUR research program. The authors would like to thank Céline Briand (SIAAP), Kheira Dahou (SIAAP), Martin Maréchal (LEESU) and Séverine Bareilles (Saur) for their help with the AC pilot and at the laboratory and Barbara Giroud (ISA) for the OMP analyses.


Syed A Ajwad
email: syed.ali.ajwad@univ-poitiers.fr

Emmanuel Moulay
email: emmanuel.moulay@univ-poitiers.fr

Michael Defoort
email: michael.defoort@uphf.fr

Tomas Ménard
email: tomas.menard@unicaen.fr

Patrick Coirault
email: patrick.coirault@univ-poitiers.fr

Leader-following consensus of second-order multi-agent systems with switching topology and partial aperiodic sampled data

Keywords: Average dwell time, Continuous-discrete time observer, Leader-follower consensus, Nonuniform and asynchronous sampling, Switching graphs I

This article focuses on the problem of leaderfollowing consensus of second-order Multi-Agent Systems (MAS) with switching topology and partial aperiodic sampled data. MAS are subject to various constraints related to information exchange among the agents. It is considered that each agent in the network is able to measure its position only and cannot measure either its velocity or acceleration (input). Moreover, the position information is sent to the neighbors at aperiodic and asynchronous sampling rates. At last, a switching communication topology among the agents is considered. An observer-based control protocol is proposed to achieve leader-following consensus for MAS with above mentioned constraints. Using an Average Dwell Time (ADT) approach, sufficient conditions are derived through Lyapunov-based stability analysis to ensure the leader-following consensus. Numerical examples are also included to show the effectiveness of the proposed scheme.

which provide better efficiency, reliability and scalability as compared to centralized controllers [START_REF] Ajwad | Output-feedback formation tracking of second-order multi-agent systems with asynchronous variable sampled data[END_REF].

The distributed consensus problem for first-order MAS has been extensively studied, for instance in [START_REF] Bliman | Average consensus problems in networks of agents with delayed communications[END_REF], [START_REF] Qu | Cooperative control of dynamical systems with application to autonomous vehicles[END_REF]. However, the results for first-order MAS cannot be directly applied for second-order MAS where agents' dynamics are governed by position and velocity. Since many physical systems can be characterized by second-order dynamics, various distributed control algorithms for second-order MAS have been proposed in literature to deal with both leaderless and leader-following consensus problems [START_REF] Zhu | On the general consensus protocol of multi-agent systems with double-integrator dynamics[END_REF], [START_REF] Yu | Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems[END_REF], [START_REF] Zhu | Leader-following consensus of second-order agents with multiple time-varying delays[END_REF], [START_REF] Tian | Fixed-time leader-follower output feedback consensus for second-order multiagent systems[END_REF].

It should be noted that most of these results consider that the communication among the agents is continuous and fixed. Moreover, it is often assumed that the agents can measure and transmit both their position and velocity states. However, these considerations are not valid for real engineering MAS applications. It is sometimes difficult to measure all states which are not even desirable due to related cost and compact sizes of the agents. Moreover, since the communication and computing equipment are digital, the information exchange between the agents cannot be continuous. Several control techniques have been proposed by the research community to deal with the consensus problem of MAS with discrete data [START_REF] Pan | Consensus of double-integrator discrete-time multi-agent system based on second-order neighbors' information[END_REF], [START_REF] Cao | Multi-vehicle coordination for double-integrator dynamics under fixed undirected/directed interaction in a sampled-data setting[END_REF]. Consensus problem with partial available data is also discussed [START_REF] Xu | Observer-based consensus tracking for second-order leader-following nonlinear multi-agent systems with adaptive coupling parameter design[END_REF], [START_REF] Yu | Second-order consensus in multi-agent dynamical systems with sampled position data[END_REF], [START_REF] Huang | Some necessary and sufficient conditions for consensus of second-order multi-agent systems with sampled position data[END_REF]. In [START_REF] Xu | Observer-based consensus tracking for second-order leader-following nonlinear multi-agent systems with adaptive coupling parameter design[END_REF], Xu et al. proposed a discontinuous observer-based leader-following protocol. Yu et al. introduced a consensus protocol by using current and previous samples of position data [START_REF] Yu | Second-order consensus in multi-agent dynamical systems with sampled position data[END_REF]. The authors of [START_REF] Huang | Some necessary and sufficient conditions for consensus of second-order multi-agent systems with sampled position data[END_REF] gave necessary and sufficient conditions to achieve consensus in MAS with sampled position information. However, in these articles, the sampling period is considered constant. In [START_REF] Zhan | Consensus in networked multiagent systems with stochastic sampling[END_REF], [START_REF] Du | Observerbased consensus for multiagent systems under stochastic sampling mechanism[END_REF], consensus algorithms have been investigated for MAS with stochastic sampling periods. However, in practical applications, the sampling could be arbitrary non-uniform as well as asynchronous where each agent has independent sampling time from the other agents in the network. Moreover, in MAS with discrete data transmission, the input is mostly kept constant. However, one can achieve continuous control input by reconstructing the state in continuous time from the discrete information. This can be obtained by using continuous-discrete time observer [START_REF] Farza | Continuous-discrete time observers for a class of mimo nonlinear systems[END_REF]. In [START_REF] Menard | Observer-based consensus for second-order multi-agent systems with arbitrary asynchronous and aperiodic sampling periods[END_REF] and [START_REF] Ajwad | Observer based leader-following consensus of second-order multi-agent systems with nonuniform sampled position data[END_REF] such observer has been used to design leaderless and leader-following control protocols respectively. However, in these articles, it is considered that the communication topology among the agents remains constant. On the other hand, it is sometimes not feasible for the agents to maintain a fixed communication topology due to various reasons like collision avoidance, communication link failure or communication range limitations etc. Therefore, in these scenarios, it is mandatory to consider switching topology. Consensus of MAS with switching topology has been discussed widely in literature e.g. [START_REF] Casadei | About disconnected topologies and synchronization of homogeneous nonlinear agents over switching networks[END_REF], [START_REF] Cai | Distributed leader-following consensus of heterogeneous second-order time-varying nonlinear multiagent systems under directed switching topology[END_REF]. However, these articles do not consider the above mentioned communication constraints of irregular and asynchronous sampling and unavailability of velocity state.

Motivated by the above discussion, in this paper, we propose a distributed leader-following consensus algorithm for second-order MAS with switching interaction topology and communication constraints. It is considered that each agent only transmits its position state to its neighbors with arbitrary non-uniform and asynchronous sampling periods. The velocity and acceleration are unavailable. Furthermore, the leader sends its position information to only a small group of followers in the network. The communication among the agents is directed. It must be noted that as compared to [START_REF] Ajwad | Observer based leader-following consensus of second-order multi-agent systems with nonuniform sampled position data[END_REF], where only fixed communication topology is considered, we assume that the interaction topology among the agents does not remain constant and changes with time. Due to the switching topology, the stability analysis becomes more complex. It should be noted that the results of [START_REF] Ajwad | Observer based leader-following consensus of second-order multi-agent systems with nonuniform sampled position data[END_REF] cannot be directly applied for the case of switching topology since switching topology can make the overall system unstable. In this paper, using an Average Dwell Time (ADT) approach, sufficient conditions are derived through Lyapunov-based stability analysis to ensure the leaderfollowing consensus.

The remaining paper is organized as follows. Preliminaries on graph theory are provided in Section II followed by the problem statement in Section III. Main results are presented in Section IV, Section V contains numerical examples and the article is concluded in Section VI.

II. RECALLS ON GRAPH THEORY

A directed graph G is a pair (V, E). The set of agents V is nonempty and finite. The set of edges E ⊆ V × V denotes ordered pairs of distinct agents. (i, j) ∈ E if agent j can receive information from agent i. A graph has a directed spanning tree if there exists a directed path from the root to all other agents. For a graph G with N agents, the adjacency matrix A = (a ij ) ∈ R N ×N with a ij = 1 if agent i can receive information from agent j and a ij = 0 otherwise; and the Laplacian matrix

L = (l ij ) ∈ R N ×N as l ii = j =i a ij , l ij = -a ij for i = j.

III. PROBLEM STATEMENT

Let us consider a MAS which consists of N followers with the following dynamics

ẋi (t) = Ax i (t) + Bu i (t), y i (t) = Cx i (t) (1)
for i = 1, . . . , N , the state is x i (t) = [r i (t) T , v i (t) T ] T where r i (t) ∈ R m is the position while v i (t) ∈ R m is the velocity of agent i. The control input of agent i is u i ∈ R m . y i ∈ R m denotes
ẋ0 (t) = Ax 0 (t), y 0 (t) = Cx 0 (t) (2)
where x 0 is the leader state and y 0 is the measured position for the leader. Definition 1: The leader-following consensus of MAS ( 1)-

(2) is achieved if lim t→∞ x i (t) -x 0 (t) = 0, i = 1 . . . N .
It is considered that each agent in the network only transmits its position r i to its neighbours at aperiodic and asynchronous time instants. The velocity v i and the input/acceleration u i are completely unavailable. Let t i,j k be the time instant at which agent j sends its position data to agent i with i = 1, . . . , N , j = 0, . . . , N (j = i) and k ∈ N. Moreover, there exist two constants τ m ≥ 0, τ M > 0 called minimum and maximum sampling time respectively such that τ m < t i,j k+1 -t i,j k < τ M . Denote G= { Ḡ1 , Ḡ2 , . . . , ḠM } as a finite set of possible topology graphs and M = {1, 2, . . . , M } represents the set of indices. Each graph in G has the same nodes (agents) but can have different edges. The switching between the graphs is time dependant and is modelled by a switching function σ(t) : [0, ∞) → M which is a piece-wise constant function, determining the topology of the dynamic network at each time instant. In this paper, it is assumed that σ(t) is generated exogenously and satisfies the minimum dwell time condition to avoid chattering and Zeno behavior in the network dynamics. Let 0 = t 0 < t 1 < t 2 . . . be the switching instants of σ(t). Furthermore, the intervals (t l , t l+1 ], l = 0, 1, . . . are bounded and contiguous. Denote the directed switching graph as G σ(t) ∈ G with A σ(t) and L σ(t) the corresponding adjacency and Laplacian matrices respectively. Let us denote the diagonal matrix B σ(t) = diag(b σ 1 (t), . . . , b σ N (t)) which represents the switching interconnection between the leader and the followers. b σ i (t), for i = 1, . . . , N is equal to 1 if agent i can receive information from the leader and zero otherwise. The switching communication graph including the followers and the leader is denoted Ḡσ(t) .

Assumption 1: Each switching graph Ḡσ(t) has a directed spanning tree with the leader as a root. Let us define matrix

H σ(t) = L σ(t) + B σ(t) . (3)
If graph Ḡσ(t) has a directed spanning tree, then H σ(t) is a nonsingular M-matrix [START_REF] Song | Pinning-controllability analysis of complex networks: an m-matrix approach[END_REF] and there exists a diagonal matrix

Ω σ = diag(ω σ 1 , . . . , ω σ N ) such that [21] H σ T Ω σ + Ω σ H σ > 0. (4)
Define the following notations

ω σ max = max{ω σ 1 , . . . , ω σ N }, (5)
ρ σ = λ min (H σ T Ω σ + Ω σ H σ ). ( 6
)
where λ min (.) denotes the smallest eigenvalue. The control objective is to design distributed consensus protocols u i (i = 1, . . . , N ), based on available aperiodic and asynchronous sampled position data such that leader-following consensus on switched dynamic network Ḡσ(t) (σ satisfies the minimum dwell time condition) is achieved according to Definition 1. To solve this problem, let us recall the following useful definition. Definition 2 ( [START_REF] Hespanha | Stability of switched systems with average dwell-time[END_REF]): For any switching signal σ(t) and t 2 > t 1 ≥ t 0 , let N σ(t2,t1) describes the number of switching of σ(t) over the time interval [t 1 , t 2 ). For any τ a > 0 and an integer

N 0 ≥ 0, if N σ(t2,t1) < N 0 + t 2 -t 1 τ a (7)
holds, then τ a is called the Average Dwell Time (ADT). Lemma 1:

[17] If v 1 (t) and v 2 (t) are real valued func- tions verifying d dt v 2 1 (t) + v 2 2 (t) ≤ -av 2 1 (t) -bv 2 2 (t) + c t t-δ v 2
2 (s)ds + k for t ≥ 0, where a, b, δ > 0 and c, k ≥ 0. There exist > 0 and ᾱ ≥ 0 such that if δ < , then v 2 1 (t) + v 2 2 (t) ≤ ᾱe -σt + k σ , ∀t ≥ 0 where σ is given by σ = 1 2 min (a, b).

IV. MAIN RESULTS

The proposed distributed control law is given as follows

u i (t) = -cK c Γ λ N j=1 a σ(t) ij [x i,i (t) -xi,j (t)] -b σ(t) i cK c Γ λ [x i,i (t) -xi,0 (t)] (8)
for i = 1, . . . , N where a

σ(t) ij
is the ij th entry of adjacency matrix A σ(t) , c is the coupling strength, K c = B T Q = I m 2I m with Q the symmetric positive definite matrix solution of algebraic Lyapunov equation [START_REF] Bédoui | Robust nonlinear controllers for bioprocesses[END_REF]

Q + QA + A T Q = QBB T Q (9)
and

Γ λ = λ 2 I m 0 m 0 m λI m
where λ is the controller tuning parameter. One should note that as compared to the control input proposed in [START_REF] Ajwad | Observer based leader-following consensus of second-order multi-agent systems with nonuniform sampled position data[END_REF], a

σ(t) ij
in ( 8) is not constant but changes with the communication graph Ḡσ(t) . xi,j (t) = [r T i,j (t), vT i,j (t)] T , i = 1, . . . , N , j = 0, . . . , N where ri,j (t) and vi,j (t) are the estimation of position and velocity respectively of agent j estimated by agent i from the available aperiodic and asynchronous sampled position data. They are computed as follows:

ẋi,j (t) =Ax i,j (t) -θ∆ -1 θ K o e -2θ(t-κi,j (t)) ri,j (κ i,j (t)) -r j (κ i,j (t)) (10
P + A T P + P A = C T C (11)
κ i,j (t) = max t i,j k | t i,j k ≤ t, k ∈ N is the last instant when agent i receives the position data of agent j. One can note that observer [START_REF] Xu | Observer-based consensus tracking for second-order leader-following nonlinear multi-agent systems with adaptive coupling parameter design[END_REF] represents a high-gain continuous-discrete time observer which estimates the state of an agent and its neighbors in continuous time from sampled aperiodic and asynchronous position information. Furthermore, since a timevarying exponential gain is used and the correcting term in the observer consists of both continuous and discrete parts, the observer dynamics ( 10) is hybrid and nonlinear.

Assumption 2: At each switching instant t l , l = 0, 1, . . . , every agent of the MAS sends its own estimated states, ri,i (t l ), vi,i (t l ), with i = 0, . . . , N , to its new neighbors. The observer updates its value at time t = t l based on the estimations it receives from the neighbors, i.e. ri,j (t l ) = rj,j (t l ) and vi,j (t l ) = vj,j (t l ).

Remark 1: Assumption 2 is important for the convergence of the observer in the case of switching graphs. It ensures that once the observer error reaches zero, it will not diverge due to switching between graphs. Also, other than switching instants, i.e. when t = t l , the observer dynamics are governed by [START_REF] Xu | Observer-based consensus tracking for second-order leader-following nonlinear multi-agent systems with adaptive coupling parameter design[END_REF]. At last, the same observer can be used by a real leader to estimate its own states which could be transmitted to its neighbors at the switching instant.

Theorem 1: Consider the MAS ( 1)-( 2) with control input (8) and let Assumptions 1 and 2 hold. If the control parameters θ, λ, c > 0 satisfy the following

θ < ¯ τ M (12) λ < * θ (13) c ≥ max p∈M {ω p max } min p∈M (ρ p ) ( 14
)
where ¯ is a positive constant, * ∈ (0, 1), ω p max and ρ p are given by ( 5) and ( 6) respectively, and if the ADT satisfies the following inequality

τ a > 8 ln (βK) -1 λ (15)
with K, β ≥ 1 are constants, then the leader-following consensus is achieved under switching dynamic network. Remark 2: The proposed leader-following algorithm is distributed since it only requires position information of the neighbors i.e only local information. Moreover, there is no centralized unit to calculate the the input of the agents. Instead each agent is computing its own input based on the discrete information it receives from the neighbors. One may remark that algorithm requires the position information in the global frame or the tuning parameters require information of communication topology. However, these are very common assumptions in designing of distributed algorithms for MAS, see for example [START_REF] Cao | An overview of recent progress in the study of distributed multi-agent coordination[END_REF], [START_REF] Ge | A survey on recent advances in distributed sampled-data cooperative control of multi-agent systems[END_REF]. Nevertheless, the tuning gains are tuned beforehand and remain constant for all t ≥ 0 and then only local information is used to compute the control input.

Proof: The proof of Theorem 1 is divided into three steps. In the first step, we consider the case of fixed topology and obtain some useful results. Then in the second step, some important results are derived for switching topology. Finally in step 3, all the flows and jumps related to switching topology are combined using previously obtained results and a condition of ADT is achieved to ensure the stability of the system.

Step 1: Consider a fixed communication graph G p (p ∈ M). Let us define the estimation error as xi,j (t) = xi,j (t) -x j (t), j = 0, . . . , N

and the tracking error as

e i (t) = x i (t) -x 0 (t), i = 1, . . . N. ( 17
)
Consider the new coordinates for classical high-gain design ēi = Γ λ e i and xi,j = ∆ θ xi,j . Denoting

η c = [ē T 1 . . . ēT N ] T , η o i = [(x i,1 ) T . . . (x i,N ) T ] T for i = 1 . . . N and η o 0 = [(x 1,0 ) T . . . (x N,0 ) T ]. Consider the following candidate Lya- punov functions V p c (η c (t)) = (η c (t)) T [Ω p ⊗ Q]η c (t) (18) V o (x i,j (t)) = (x i,j (t)) T P xi,j (t) (19)
Vo (η o (t)) = N i=1 N j=0 V o (x i,j (t)) (20)
Taking the derivative of the above Lyapunov functions and applying Lemma 1, the following inequality is achieved if conditions ( 12)-( 14) and Assumption 1 are satisfied (please see [START_REF] Ajwad | Observer based leader-following consensus of second-order multi-agent systems with nonuniform sampled position data[END_REF] for more details)

V p c (η c (t)) + 3 2 θ 2 Vo (η o (t)) ≤ ᾱ(t 0 )e -λ 8 (t-t0) (21)
where ᾱ(t 0 ) is given as

ᾱ(t 0 ) = V p c (η c (t 0 )) + 3 2 θ 2 V0 (η o (t 0 )) + c 3 2 θ 2 × τ M 0 t0 t0-s e vκ(µ-t0+s) V0 (µ)dµds (22)
where c > 0, v ≥ 0 and κ ≥ 0 (see Lemma 3 of [START_REF] Ajwad | Observer based leader-following consensus of second-order multi-agent systems with nonuniform sampled position data[END_REF] for details).

It is clear from (21) that the system achieves stability for a fixed communication topology. However, this does not imply that the closed-loop system will remain stable in the case of switching communication topology since switching may lead to an overall unstable system. Therefore, we need to find out the stability conditions considering switching topology. We first need the following results. Considering time interval t ∈ [t 0 , t 1 ) and using ( 22), ( 21) can be written as:

V p c (η c (t)) + 3 2 θ 2 V0 (t) (23)
≤ V p c (η c (t 0 )) + 3 2 θ 2 K max s∈[t0-τ M ,t0] Vo (s) e -λ 8 (t-t0)
so one can obtain the following

V p c (η c (t 1 )) + 3 2 θ 2 max s∈[t1-τ M ,t1) V0 (s) ≤ V p c (η c (t 0 )) + 3 2 θ 2 K max s∈[t0-τ M ,t0] Vo (s) × e λ 8 τ M e -λ 8 (t1-t0) (24)
with K = max{1, cτ 2 M e vκτ M }. V p c satisfies the following properties [START_REF] Chen | Second-order consensus of nonlinear multi-agent systems with restricted switching topology and time delay[END_REF], [START_REF] Gao | Distributed reduced-order observerbased approach to consensus problems for linear multi-agent systems[END_REF]:

• Since ω i ⊗ Q is always symmetric positive definite for any i ∈ M, there exists β ≥ 1 such that V p c ≤ β V q c , ∀p, q ∈ M (25) so V p c ≤ β V q c , ∀p, q ∈ M (26)
where β = β;

• Let α 1 = min p∈M (λ min (Ω p ⊗ Q)) and α 2 = max p∈M (λ max (Ω p ⊗ Q)), then α 1 η c 2 ≤ V p c ≤ α 2 η c 2 . ( 27
)
Step 2: Let us now define a piecewise Lyapunov function for the considered switching communication topology

V σ(t) c (η c (t)) = (η c (t)) T [Ω σ(t) ⊗ Q]η c (t). (28)
Then, from [START_REF] Ge | A survey on recent advances in distributed sampled-data cooperative control of multi-agent systems[END_REF], for any switching instant t l , l = 1, 2, . . . , one can get

V σ(t l ) c (η c (t l )) ≤ β V σ(t - l ) c (η c (t - l )). (29)
Furthermore, if Assumption 2 is satisfied, one has

V0 (η o (t l )) = V0 (η o (t - l )). (30)
Hence, one can obtain

V σ(t l ) c (η c ) + 3 2 θ 2 max s∈[t l ,t l -τ M ) Vo (s) (31)
≤ β V σ(t - l ) c (η c ) + 3 2 θ 2 max s∈[t - l ,t - l -τ M )
Vo (s)

Step 3: For t ∈ [t k , t k+1 ), from ( 23) and (31), one has

V σ(t) c (η c ) + 3 2 θ 2 max s∈[t-τ M ,t) V0 (s) ≤ e λ 8 τ M V σ(t k ) c (η c ) + 3 2 θ 2 K max s∈[t k -τ M ,t k ] Vo (s) e -λ 8 (t-t k ) (32)
≤ βKe

λ 8 τ M V σ(t - k ) c (η c ) + 3 2 θ 2 max s∈[t - k -τ M ,t - k ] Vo (s) e -λ 8 (t-t k ) (33) ≤ βK 2 e 2 λ 8 τ M V σ(t0) c (η c (t k-1 )) + 3 2 θ 2 max s∈[t k-1 -τ M ,t k-1 ] Vo (s) e -λ 8 (t-t k-1 ) ≤ β Nσ (Ke λ 8 τ M ) Nσ+1 V σ(t0) c (η c ) + 3 2 θ 2 max s∈[t0-τ M ,t0] Vo (s) e -λ 8 (t-t0) ≤ β N0 (Ke λ 8 τ M ) N0+1 (βK) t-t 0 τa e t-t 0 τa V σ(t0) c (η c ) + 3 2 θ 2 max s∈[t0-τ M ,t0] Vo (s) e -λ 8 (t-t0)
Now, using Definition 2, one has

V σ(t) c (η c ) + 3 2 θ 2 max s∈[t-τ M ,t) V0 (s) ≤ β N0 (Ke λ 8 τ M ) N0+1 V σ(t0) c (η c ) (34) + 3 2 θ 2 max s∈[t0-τ M ,t0] Vo (s) e -( λ 8 - ln (βK)-1 τa )(t-t0)
Hence, if the ADT satisfies condition [START_REF] Farza | Continuous-discrete time observers for a class of mimo nonlinear systems[END_REF], system (1)-( 2) achieves leader-following consensus under switching dynamic network. From the original coordinates of tracking error, we can achieve the following inequality:

N i=1 e i ≤ l 1 V σ(t) c (η c ) (35)
with

l 1 = 1 λ √ N √ λmin(Q) ω σ(t) min
. From the over-valuation of (34) and using (35), we achieve

N i=1 e i ≤ l 1 γe -( λ 8 - ln (βK)-1 τa )(t-t0) (36)
where γ = β N0 (Ke

λ 8 τ M ) N0+1 V σ(t0) c (η c ) + 3 2 θ 2 max s∈[t0-τ M ,t0] Vo (s)
. It is clear from (36) that if ADT satisfies condition [START_REF] Farza | Continuous-discrete time observers for a class of mimo nonlinear systems[END_REF], the tracking error decays exponentially.

V. SIMULATIONS

We consider a MAS with 4 followers labelled from 1 to 4 and a leader labelled 0 for simulation purposes. Three possible communication topologies are shown in Figure 1. The topologies are switching according to the switching signal In the first case, the leader is kept stationary. Figure 3-(

VI. CONCLUSION

In this paper, we study the problem of leader-following consensus of second-order MAS with switching topology. The agents cannot measure their velocity and acceleration. They only share their position state with neighbors in a discrete aperiodic and asynchronous way. Using an ADT approach, sufficient conditions are derived through Lyapunov-based stability analysis to design an observer-based control protocol which solves the leader-following consensus. The investigation of the case where individual graphs do not necessarily have a spanning tree but only a joint-graph containing a spanning tree in a time period is considered for future work.

  Considering the directed graph combining both the leader and the followers, denoted by Ḡ, one can define the pinning matrix as the diagonal matrix B = diag(b 1 , b 2 , . . . , b N ) with b j = 1 if follower j can receive information from the leader and b j = 0 otherwise.

  the measured position for agent i. Note that the position data are transmitted between agents according to the communication topology in a discrete aperiodic way. A = 0 m I m 0 m 0 m , B = 0 m I m and C = I m 0 m are the system input and output matrices, respectively. The leader agent has the following dynamics

) where θ represents the observer tuning parameter while ∆ θ = I m 0 m 0 m 1 θ

 1 I m and K o = P -1 C T = 2I m I mT , with P the symmetric positive definite matrix solution of the algebraic Lyapunov equation[START_REF] Gauthier | A simple observer for nonlinear systems applications to bioreactors[END_REF]

Fig. 1 :

 1 Fig. 1: Communication graphs

Fig. 3 :Fig. 4 :Fig. 5 :

 345 Fig. 3: Leader following consensus with a stationary leader (a) position consensus -(b) velocity consensus

Fig. 6 :

 6 Fig. 6: Tracking errors for consensus with a moving leader

Fig. 7 :

 7 Fig. 7: Sampling periods for data transmission between the leader and follower 1