Magali Aubert
email: magali.aubert@inra.fr

Orane Debrune
email: orane.debrune@cirad.fr

Joël Huat
email: joel.huat@cirad.fr

Laurent Parrot
email: laurent.parrot@cirad.fr

Laurent Parrot The

The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte

Keywords: Mayotte, tomato, agro-ecology, formal agriculture, logit model

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

Introduction

While the use of pesticide increases yield and the income of farmers, the counterpart of such utilization is the negative impact on both health and the environment [START_REF] Aktar | Impact of pesticides use in agriculture: their benefits and hazards[END_REF][START_REF] Inserm | Pesticides -Effets sur la santé[END_REF]. Because of these negative effects, public authorities define and impose phytosanitary requirements to guarantee products' safety.

In 1992, a reform of the Common Agricultural Policy considered the environmental dimension to avoid harmful agricultural activity by providing mainly financial incentives. Progressively, the European policy takes into account an agricultural model dedicated to the implementation of environmental-friendly practices1 . Consideration of biodiversity, landscapes, climate change, air and water quality became an integral part of European policy guidelines. Progressively, price and production supports evolved into direct aid policies and rural development measures, reducing the pressure to produce more and intensify the use of pesticides. Agri-environmental measures or green payments are supposed to promote agricultural economic development through the environment, since the rules imputed for access to these public subsidies are respected. In addition to financial incentives, Europe is committed to reducing the risks of exposure to pesticides. In 2005, Regulation (EC) No 396/2005 defines Maximum Residue Limits (MRLs) for authorized active substances in food in order to reduce the exposure of consumers to excessively high product doses (European Commission, 2008). In 2009, Europe adopted the "pesticide package": each Member State has to define a national action plan aimed at reducing mainly the use of pesticides.

France is the first european country consuming pesticides [START_REF] Aubertot | Pesticides, agriculture et environnement : Réduire l'utilisation des pesticides et en limiter les impacts environnementaux[END_REF]. To reduce the use of pesticides, France implemented the national action plan Ecophyto 2018 and Ecophyto 2025, launched and co-piloted by the Ministry of Agriculture. The first 2018 plan whose aim was to reduce quantitatively the use of pesticides did not achieve its objectives [START_REF] Potier | Pesticides et agro-écologie : Les champs du possible[END_REF]. Hence, a second plan adopted both quantitative and qualitative objectives. This second plan aims at reducing if possible by 50 % by 2025 the use of pesticides incitating producers to adopt environmental-friendly practices and involving all actors of the sector.

It is through the development of agro-ecology supported by the Agricultural Ministry in 2012 that a new model appeared as a guideline of French agricultural development. Defined as "the application of ecological science to the study, design and management of sustainable agrosystems" by the French government, agro-ecology is a "set of agricultural practices favoring biological interactions aiming at optimizing the use of the possibilities offered by agrosystems " (Direction de l'information légale et administrative de la République, 2015). This approach aims to combine the productivity of the agricultural sector and the rational use of natural resources. Wherever possible, the pesticides used must be replaced by natural processes. Improving soil quality, maximizing ecosystem services, optimizing farm resilience and, indirectly, reducing health risks, are the main objectives targeted by agroecology [START_REF] Schutter | Agroécologie et droit à l'alimentation[END_REF][START_REF] Altieri | The scaling up of agroecology : spreading the hope for food sovereignty and resiliency A contribution to discussions at Rio + 20 on issues at the interface of hunger , agriculture , environment and social prepared by The scaling up of agroecology : spread[END_REF][START_REF] Silici | Agroecology. What It Is And What It Has To Offer[END_REF].

Comment citer ce document : Aubert, M., Debrune, O., Huat, J., Parrot, L. ( 2017). The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte. Presented at 11. Journées de Recherches en Sciences Sociales (JRSS), Lyon, FRA (2017-12-14 -2017-12-15) .

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The evolution of European and national requirements in terms of phytosanitary reduction means a change in the practices of producers. It should be noted that if all the national territory is concerned by these requirements, Mayotte island is a privileged field of study since it is a French department only since 2011 and an overseas region since 2014. Hence, the harmonization of these practices with European and national regulations is recent [START_REF] Sourisseau | Changement institutionnel et agriculture à Mayotte Les impacts d ' une intégration renforcée à la République française sur l ' activité agricole des ménages[END_REF]. The compliance of the agricultural practices of Mahorais to the health and environmental requirements is far from reaching the expected levels and there still exists an inadequacy between what is practiced and what should be [START_REF] Daaf | Analyse des pratiques en maraîchage[END_REF].

Mayotte is a relevant case study because of its recent integration at the French and European level. Mayotte is also relevant since its history translates into a co-existence between legal and illegal population and between formal and non-formal one. Farmers who can benefit from technical and financial support are formal ones: farmers who have a SIRET number (the French Computer System for the Business Directory on the Territory). Because of this potential support and the implication of such support, our study focuses on formal farmers who represent 20 % of the total agricultural production.

In Mayotte, the main crop using pesticides is the tomato. Hence, our study focuses on this production and more precisely on field tomato production since it is the more sensible one to pest. This production is a seasonal and perishable one.

The aim of this study is to analyze to what extent Mahorais' farmers are affected by the evolution of phytosanitary requirements and to what extent they will be inclined to adopt alternative practices. The first part of this study is the explanation of the Mahorais' context. The second part aims at identifying, through a literature review, factors that condition the farmers' behaviour and more precisely their propension to adopt environmental-friendly practices. The third part defines data and methods. This part declines the two surveys performed, the sampling methodology adopted and the econometric model implemented. The first one consisted in interviews among the main actors of the sector and the second survey covered formal farmers. While the first survey aimed at describing the organization of the sector, the second survey identified opportunities and constraints for the implementation of environmental-friendly practices. Since fourty-seven farmers were surveyed, the econometric model used a bootstrap sampling even if these farmers represent almost all the formal population. The last part puts into perspective the results issued from this model, at the farmer level, with results from the first survey.

Background

Mayotte is a 375 km² group of island located in the Indian Ocean, 300 km away from Madagascar and 500 km East of Africa next to the Mozambique canal. The archipelago, composed of 2 main island (Grande-Terre and Petite-Terre), is situated between the equator and the Capricorn tropic, 8 000 km away from France. Mayotte is a relevant case study, since this insularity represents numerous constraints reflected in every small island economy such Comment citer ce document : Aubert, M., Debrune, O., Huat, J., Parrot, L. ( 2017). The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte. Presented at 11. Journées de Recherches en Sciences Sociales (JRSS), Lyon, FRA (2017-12-14 -2017-12-15) .

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as vulnerability to naturals and economic exogenous chocks, high transport cost, dependency to product or services from others countries. It makes difficult industrialization, diversification and competitiveness on the island [START_REF] Rivière | Mutations et évolutions de l'économie mahoraise à la veille de la départementalisation[END_REF]. Because Mayotte acquired in 2011 the French Overseas Department status followed by the status of Ultraperipherial Region of Europe, in 2014 January1 st , the political, financial and economic framework is evolving.

Therefore, a departmentalization process has been engaged with a legal, economic, legislative and social retrofit in order to achieve European and National requirements [START_REF] Sourisseau | Changement institutionnel et agriculture à Mayotte Les impacts d ' une intégration renforcée à la République française sur l ' activité agricole des ménages[END_REF] In Mayotte, exclusively used on horticultural crops [START_REF] Daaf | Analyse des pratiques en maraîchage[END_REF], pesticides are at the heart of local preoccupation and territories challenges. The vegetable sector is one of the most dynamic on the island, representing 1, 9% of total cultivated area and 8% of farms. These cash crops, because they provide fast financial flow due to their short production cycle, attract an increasing number of producers: around 40 ha in 2003 and 130 ha in 2010 [START_REF] Daaf | Synthèse illustrée du recensement agricole[END_REF]. Produced for local consumption, horticultural crops keep growing to respond to the 2011 riot "against expensive life" to reduce importations and enhancing island food security potential. However, climate seasonality (southern summer and southern winter) guide the productive strategies of farmers [START_REF] Daaf | Programme portant mesures spécifiques dans le domane de l'agriculture en faveur des régions Ultrapériphériques[END_REF]. Heavy rainfalls during southern summer limit the full-field production, at the origin of high variation of price during the year. It is particularly the case for tomatoes production, the most represented on the island : 44% of horticultural farm produce tomatoes and 93% is in open-filed (or 58 ha of the total agricultural area) [START_REF] Daaf | Synthèse illustrée du recensement agricole[END_REF]. It is exclusively produced during the dry season (from June to September), when agroclimatic conditions are the most favorable. However, during this season, tomato production is highly impacted by Neoceratitis cyanescens (Diptera: Tephritidae). This insect fly causes major damage to Solanaceae crops, mainly tomato. Yield losses can reach 80% [START_REF] Huat | Limiting factors for yields of field tomatoes grown by smallholders in tropical regions[END_REF]. The fly pricks the fruit to lay its eggs. Larvae as well as other pathogen penetrate in the injuried fruit, rotting the fruit, which is then no longer consumable [START_REF] Brevault | Mécanismes de localisation de l'hôte chez la mouche de la tomate[END_REF].

Comment citer ce document : Aubert, M., Debrune, O., Huat, J., Parrot, L. ( 2017). The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte. Presented at 11. Journées de Recherches en Sciences Sociales (JRSS), Lyon, FRA (2017-12-14 -2017-12-15) .

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Chemical responses are essentially used against Neoceratitis cyanescens. Nor specific, nor selective, products mainly used on the island (lambda-cyhalothrine et deltaméthrine) master only partially the pest [START_REF] Ryckewaert | Lutte integrée contre les ravageurs des cultures maraîchères a la reunion[END_REF]. Rules defined by the European directive for phytosanitary use (maximal dose of use, number of application, pre-harvest delay, physical protection) are not respected by every producer on the island [START_REF] Didelot | Le plan Ecophyto à Mayotte -exemple du maraîchage[END_REF]. A treatment frequency index, 4 to 8 times higher than in mainland France, has been observed in certain case. Products use, which are not always allowed in France, and supposed being distributed through official center with a Certiphyto, are still present in numerous farms. However, only 20% of them are legal and can buy chemical products in official distribution networks. This highlights the importance of an informal supply system: illegal importations of products from bordering islands allow farms to easily have access to them.

Contrary to a solid control system in France mainland, few control are realized in Mayotte before selling the product. Tomatoes value chain is not structured since 90% of the selling is done through informal trade networks, nor respecting the maximal residues limit, nor the traceability on origin or quality of the product. Rather than that, producers as well as consumers follow an opportunist logic, creating a low competitiveness in the tomatoes sector. With the limited market of the island, the atomization and the seasonality of the offer, the local economy is destabilized. The formal sector which requires quantity and quality standards encounters difficulty to expand.

Even though there is an important use of pesticides in Mayotte, few technics are available and known by farmers to effectively fight the fly. This production is essential in mahorais' consumption habits and reduce imports is another stake that has to be controlled. Agricultural practices evolution should in consequence pass by integration of innovative practices in production systems. Nets are an example where their benefits have already been highlighted in Kenya and Benin, in terms of agronomic productivity (pest number reduction, yield increase) [START_REF] Martin | Efficacy of Mosquito Netting for Sustainable Small Holders ' Cabbage Production in Africa[END_REF][START_REF] Muleke | Enhancing Cabbage ( Brassica oleraceae Var capitata ) Yields and Quality Through Microclimate Modification and Physiological Improvement Using Agronet Covers[END_REF] and economic viability [START_REF] Martin | Efficacy of Mosquito Netting for Sustainable Small Holders ' Cabbage Production in Africa[END_REF][START_REF] Martin | Eco-friendly nets to improve vegetable production and quality in sub-Saharan Africa[END_REF][START_REF] Vidogbéna | Cost: Benefit analysis of insect net use in cabbage in real farming conditions among smallholder farmers in Benin[END_REF]. Adoption of agro-ecological practices to answer the requirements of European rules could however be difficult to reach. In order to achieve mahorais'food habit, development of new market, increasing population and demand from supermarket to have access to fresh fruit and vegetables, it is important to understand personal, structural, institutional determinants of farmers deciding their productive strategy.

Theoretical framework

In this section, we consider the definition of more environmental-friendly practices before considering the determinants of the implementation of such practices. "Environmentalfriendly practices" is a terminology that embraces different behaviours from the adoption of a certificate [START_REF] Chemnitz | The compliance decision with food quality standards on primary producer level. A case study of the EUREPGAP Standard in the Moroccan tomato sector[END_REF][START_REF] Dörr | Impact of certification on fruit producers in the Sao Francisco Valley in Brazil[END_REF][START_REF] Asfaw | What impact are EU supermarket standards having on developing countries export of high value horticultural products? Evidence from Kenya[END_REF][START_REF] Kersting | Public-private partnerships and GLOBALGAP standard adoption: evidence from small-scale fruit and vegetable farmers in Thailand[END_REF][START_REF] Zhou | Implementation of food safety and quality standards: A case study of vegetable processing industry in Zhejiang, China[END_REF] to the implementation of a specific practice [START_REF] Okoye | Comparative analysis of factors in the adoption of traditional and recommended soil reosion control practices in Nigeria[END_REF][START_REF] Traoré | On-farm adoption of conservation practices: The role of farm and farmer characteristics[END_REF][START_REF] Fernandez-Cornejo | The environmental effects of adopting IPM techniques: The case of peach producers[END_REF][START_REF] Pereira De Herrera | Adoption of maize conservation tillage in Azuero, Panama[END_REF][START_REF] Galt | Toward an Integrated understanding of pesticide use Intensity in Costa Rican vegetable farming[END_REF][START_REF] Sharma | Impact evaluation indicators of an Integrated Pest Management program in vegetable crops in the subtropical region of Jammu and Kashmir, India[END_REF] such as the use of nets to protect production from insects.

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To understand to what extend farmers are more or less likely to implement environmentalfriendly practices, an analysis of the literature let us appreciate brakes and leverages of this productive choice. The determinants related to the implementation of more environmentalfriendly practices are largely studied in the literature. From developing countries to developed ones, all studies highlight the importance of farmers' characteristics (Hypothesis 1), their farm characteristics (Hypothesis 2), their financial dimension (Hypothesis 3) and their geographical location (Hypothesis 4). Since these characteristics are unanimously considered, our study focuses on others determinants less studies in the literature: on one hand the hazard perception of farmers (Hypothesis 5) and the institutional environment on which farmers' evolve (Hypothesis 6). These hypotheses are summarized in Figure 1. The main characteristic of the farmers considered is their age [START_REF] Fernandez-Cornejo | The environmental effects of adopting IPM techniques: The case of peach producers[END_REF][START_REF] Dörr | Impact of certification on fruit producers in the Sao Francisco Valley in Brazil[END_REF][START_REF] Asfaw | What impact are EU supermarket standards having on developing countries export of high value horticultural products? Evidence from Kenya[END_REF][START_REF] Kersting | Public-private partnerships and GLOBALGAP standard adoption: evidence from small-scale fruit and vegetable farmers in Thailand[END_REF][START_REF] Sharma | Technology adoption and pest control: strategies among UK cereal farmers: Evidence from parametric and nonparametric count data models[END_REF]. Almost all studies underline the fact that younger farmers are more aware with the impact of pesticides on environment. They are supposed to be more educated to these impacts and be more likely able to estimate the positive impact of the implementation of an environmental-friendly practice. Hence, we hypothesize that:

Younger farmers are more likely to implement environmental-friendly practices.

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Another individual characteristic taken into account is the fact that farmers have, or not, off-farm activity. The impact of such activity has an ambivalent impact since on one hand this can translate into a higher income letting the farmer more likely to implement more environmental-friendly practices [START_REF] Clay | Sustainable intensification in the highland tropics: Rwandan farmers' investments in land conservation and soil fertility[END_REF][START_REF] Knowler | Farmers' adoption of conservation agriculture: A review and synthesis of recent research[END_REF][START_REF] Galt | Toward an Integrated understanding of pesticide use Intensity in Costa Rican vegetable farming[END_REF] and on the other hand this can translate into a lower implication of the farmer on his farm leading to a less probability to implement these practices [START_REF] Gould | Conservation tillage: The role of farm and operator characteristics and the perception of soil erosion[END_REF]. Since the main brakes declared by Mahorais' farmers to the adoption of alternative strategies is the price, we assume here that:

Farmers who have off-farm activity are more likely to implement environmental-friendly practices.

-Hypothesis 2: Farms' characteristics Beyond individual characteristics of the farmers, the literature assumes that the characteristics of the farms have also an influence on farmers' behaviour. More precisely, the area cultivated is the only unanimous factor considered. Therefore, while there is unanimity with the fact that area is an essential information to take into account, its impact on the implementation of more environmental-friendly practices is controversial. Some authors consider that bigger farms benefit from economy of scale and are hence more likely to implement these practices [START_REF] Feder | Adoption of agricultural innovations in developping countries : A survey[END_REF][START_REF] Fernandez-Cornejo | The adoption of IPM techniques by vegetable growers in Florida, Michigan and Texas[END_REF][START_REF] Galt | Toward an Integrated understanding of pesticide use Intensity in Costa Rican vegetable farming[END_REF][START_REF] Asfaw | What impact are EU supermarket standards having on developing countries export of high value horticultural products? Evidence from Kenya[END_REF][START_REF] Zhou | Implementation of food safety and quality standards: A case study of vegetable processing industry in Zhejiang, China[END_REF]. Others consider that smaller farms are more inclined to implement such practices [START_REF] Clay | Sustainable intensification in the highland tropics: Rwandan farmers' investments in land conservation and soil fertility[END_REF][START_REF] Enjolras | The determinants of chemical input use in agriculture : A dynamic of the wine grape-growing sector in France[END_REF]. In the Mahorais' context, where the access to land is quite difficult, we consider the physical dimension of the farm through the workforce employed. Hence, we assume that:

Farms, which employ more workforce are more likely to implement environmental-friendly practices.

The second characteristic considered is the degree of crop diversification. As a matter of fact, the more farmers are crop diversified on one production, the less they are economically dependent from this activity [START_REF] Laughlin | The impact of agricultural practices on biodiversity[END_REF][START_REF] Altieri | Ecological impacts of industrial agriculture and the possibilities for truly sustainable farming[END_REF][START_REF] Roschewitz | Are landscape complexity and farm specialization related to land-use intensity of annual crop fiels ?[END_REF][START_REF] Dörr | Impact of certification on fruit producers in the Sao Francisco Valley in Brazil[END_REF]. In such a case, they are more likely to implement environmentalfriendly practices. This point is reinforced by the fact that being diversified translates into a less parasite pressure.

Diversified farms are more likely to implement environmental-friendly practices.

-Hypothesis 3: Financial dimension Individual characteristics of farmers and characteristics of their farm are the two main items considered in the literature to understand to what extend they are more or less likely to implement environmental-friendly practices. More than these characteristics, the financial dimension needs to be highlighted [START_REF] Nowak | Why farmers adopt production technology[END_REF][START_REF] Clay | Sustainable intensification in the highland tropics: Rwandan farmers' investments in land conservation and soil fertility[END_REF][START_REF] Okoye | Comparative analysis of factors in the adoption of traditional and recommended soil reosion control practices in Nigeria[END_REF][START_REF] Knowler | Farmers' adoption of conservation agriculture: A review and synthesis of recent research[END_REF] Comment citer ce document : Aubert, M., Debrune, O., Huat, J., Parrot, L. ( 2017). The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte. Presented at 11. Journées de Recherches en Sciences Sociales (JRSS), Lyon, FRA (2017-12-14 -2017-12-15) .

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et [START_REF] Knowler | Farmers' adoption of conservation agriculture: A review and synthesis of recent research[END_REF]. As a matter of fact, farmers who benefit from financial support of Common Agricultural Policy or who benefit from credit access are more likely to invest to answer phytosanitary requirements.

Farmers who benefit from any support are more likely to implement environmental-friendly practices.

-Hypothesis 4: Location More than active variables, some are considered as controlled variables since farmers cannot modify them [START_REF] Houmy | Importance des conditions climatiques dans l'applictaion des produits phytosanitaires[END_REF][START_REF] Rosenzweig | Climate change and extreme weather events : Implications for food production, plant diseases and pests[END_REF][START_REF] Koleva | The impact of weather variablibity and climate change on pesticide applications in the US : An empirical investigation[END_REF]. The location is one of these variables. The location incorporates several characteristics that can appear as opportunities or constraints for the implementation of environmental-friendly practices. We have to notice that all opportunities become constraints once they are missing. A first constraint for the adoption of an alternative strategy is the access to water. A second opportunity for the adoption of an alternative production strategy refers to the infrastructural characteristics and more precisely to the access to paved roads. The last leverage identified is the access to plots. Some farmers have plots with a slope of more than 15 % [START_REF] Daaf | Synthèse illustrée du recensement agricole[END_REF]. Farming on these plots is hence more complicated and does not facilitate the implementation of environmental-friendly practices. We assume that farmers have to adapt to their geographical environment.

Farmers' behaviour in terms of use of pesticides is conditioned by their geographical location -Hypothesis 5: Hazard perception

In the literature, few authors take into account the hazard perception of farmers. Any innovation or newness translates into some degree of uncertainty [START_REF] Rogers | Diffusion of innovations[END_REF][START_REF] Ervin | Factors affecting the use of soil conservation practices : Hypotheses, evidence and policy implications[END_REF][START_REF] Mcdonald | Difficulties in measuring adoption of apple IPM : A case study[END_REF][START_REF] Traoré | On-farm adoption of conservation practices: The role of farm and farmer characteristics[END_REF][START_REF] Lefebvre | Incentives and policies for integrated pest management in Europe : a review[END_REF]. As a matter of fact, this perception is quite difficult to measure and national surveys let not appreciate this subjective information. A way to quantify the risk perceived by the producers is to consider the risk related to the use of pesticides on health. Farmers whose entourage has suffered from the consumption of contaminated products are more aware to the impact of pesticide used than others [START_REF] Traoré | On-farm adoption of conservation practices: The role of farm and farmer characteristics[END_REF][START_REF] Li | Analysis of food poisoning due to taking vegetable contaminated with organophosphorus pesticide[END_REF][START_REF] Deng | Survey of food poisonning by organophosphorus pesticide at the employee refectory[END_REF][START_REF] Zhou | Implementation of food safety and quality standards: A case study of vegetable processing industry in Zhejiang, China[END_REF]. We assume that:

Farmers whose entourage has suffer from the consumption of contaminated products are more likely to implement environmental-friendly practices.

-Hypothesis 6: Institutional environment More than characteristics related to the farmers and their farm, the institutional environment in which they evolve can favour the implementation of environmental-friendly practices. For the tomato production, a way to appreciate the support of institutional Comment citer ce document : Aubert, M., Debrune, O., Huat, J., Parrot, L. ( 2017). The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte. Presented at 11. Journées de Recherches en Sciences Sociales (JRSS), Lyon, FRA (2017-12-14 -2017-12-15) .

10 environment is the access to technical support [START_REF] Mcdonald | Difficulties in measuring adoption of apple IPM : A case study[END_REF][START_REF] Traoré | On-farm adoption of conservation practices: The role of farm and farmer characteristics[END_REF][START_REF] Pereira De Herrera | Adoption of maize conservation tillage in Azuero, Panama[END_REF][START_REF] Adsadpur | Socio-economic factors affecting the development of biological technologies stem borer pest in rice fields of Mazandaran[END_REF]. More precisely, farmers can declare to have no access, or have an informal or a formal access. Formal access is defined by any official structure such as cooperatives or DAAF.

Farmers who have access to information through a formal way are more likely to implement environmental-friendly practices.

All variables considered are presented in Table 1.

Material and method

Two surveys were performed. The first one is a qualitative survey whose aim is both to identify farmers producing tomatoes and to appropriate the organisation of this sector. The second one is a quantitative survey performed at the farmers' level to understand to what extend they are likely to adopt alternative practices.

Comment citer ce document : Aubert, M., Debrune, O., Huat, J., Parrot, L. ( 2017). The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte. Presented at 11. Journées de Recherches en Sciences Sociales (JRSS), Lyon, FRA (2017-12-14 -2017-12-15) .

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Qualitative survey to appropriate the organization of the tomato's sector

To understand the organization of the tomato's sector, almost all structures were surveyed. More precisely six institutional structures and one non-institutional structure were surveyed:

-The cooperative COOPAC is the main cooperative for tomatoes' producers.

-The AEM (Agri-Evolution Mahorais) is a producers group interested in the market gardeners and poultry. -The DEPHY network whose aim is to support producers who want to implement alternatives practices to reduce their use of pesticides. -The agricultural secondary school, which takes over mainly an epidemiology monitoring and follows the evolution of parasite pressure for market gardeners. -The syndicate 'Jeunes agriculteurs' helps producers for their installation.

-The CIRAD, which has an expertise in term of market gardeners.

More than these institutional structures, one association was surveyed: the "Saveurs et Senteurs de Mayotte". This organization of manufacturers coordinates a network to help producers transforming their production through a collective manufacturing center or to help producers being in relation with manufacturers of fresh fruits and vegetables. The main objective is to enhance local production through a value chain more structured. Hence, we surveyed these manufacturers and their suppliers.

All information collected was put into perspective to understand the organization of the tomato's sector and to identify formal farmers producing tomatoes. These information's let us position more precisely the farmers environment.

Quantitative survey to understand to what extend farmers are likely to

implement environmental-friendly practices

Sampling methodology

The agricultural census performed in 2010 in Mayotte identified all farms producing more than 1 hectare 4 or more than 0.2 hectare of specialized production. Since we can make the hypothesis that from 2010 to 2017 the Mahorais's landscape has evolved and since we have no more recent data to position our sample, we position our sampling to this last census, with all bias that can occur because of this evolution.

To identify tomatoes' producers, the qualitative survey let us identify the base of our first sample. From this one, all producers were surveyed, other tomato producers were identified with a snowball sampling methodology. To complete our sample, agricultural markets where visited and each seller was asked to tell us the name of their suppliers. 2017). The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte. Presented at 11. Journées de Recherches en Sciences Sociales (JRSS), Lyon, FRA (2017-12-14 -2017-12-15) .

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To insure the validity of our sample and insure that producers surveyed represent almost all the formal population (farmers who have a SIRET identification), we compared the tomato area of our sample with the tomato area identified through the agricultural census. The concordance between these areas let us think that almost all formal field farmers were surveyed.

Econometric model

The aim of our study is to understand to what extend tomatoes' producers are inclined to implement more environmental-friendly practices depending the individual and structural characteristics and conditioned by their institutional environment. To understand this dual choice, a logit model is implemented. This model let us differentiate farmers who use pesticides from others. Formally, this model can be written as follow:

𝑌 ! = 1 𝑖𝑓 𝑌 ! * > 0; 𝑂 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
And:

𝑌 ! * = 𝛼 + 𝛽𝐼𝐶 ! + 𝛾𝑆𝐶 ! + 𝜁𝐹𝐶 ! + 𝜃𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛 ! + 𝜆𝐻𝑃 ! + 𝛿𝐼𝐸 ! + 𝜀 !
Where: 𝑌 ! * is the choice done by the farmer to use, or not, pesticides 𝛽 is the coefficients associated to individual characteristics, denoted 𝐼𝐶 ! 𝛾 is the coefficients associated to structural characteristics, denoted 𝑆𝐶 ! 𝜁 is the coefficients associated to financial characteristics, denoted 𝐹𝐶 ! 𝜃 is the coefficients associated to location, denoted 𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛 ! 𝜆 is the coefficients associated to hazard perception, denoted 𝐻𝑃 ! 𝛿 is the coefficient associated to the institutional environment in which the farmer evolves, denotes 𝐸𝐼 ! 𝜀 ! is the error term

The Bootstrap resampling method

Even though producers surveyed are exhaustive, their number is not sufficient to implement an econometric model that leads to robust results. To compensate this lack of observations, we implement the Bootstrap resampling method. The aim of such method is usually summarized as follow: "to put oneself up by one's bootstrap". As a matter of fact, such process let create information by information contained in the initial database, thanks to a random draw. The new database let implement statistical inference. This methodology is used in case of empirical samples [START_REF] Davidson | Estimation and Inference in Econometrics[END_REF][START_REF] Vial | Loisirs de pleine nature et utilisation des territoires : Le cas des activités équestres diffuses[END_REF].

Comment citer ce document : Aubert, M., Debrune, O., Huat, J., Parrot, L. ( 2017). The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte. Presented at 11. Journées de Recherches en Sciences Sociales (JRSS), Lyon, FRA (2017-12-14 -2017-12-15) .

13

Considering a vector x that can be denoted as follow: 𝑥 = (𝑥 ! … 𝑥 ! ), B bootstrap sampling can be performed where one new vector is denoted 𝑥 * = (𝑥 ! * … 𝑥 ! * ). An empirical rule estimates the number of B optimal to guarantee the quality of results: from 25 estimations we obtain a first estimation and from 50 we obtain relevant estimations [START_REF] Efron | An Introduction to Bootstrap[END_REF].

In our study, we first 50 samples constituted by 100 replications and then 50 samples constituted by 150 replications of the initial database. From the simulations performed, we compared the results obtained to validate the results robustness.

Policy implications

Since econometric results confirm statistics elements (Table 2 andTable 3), our reading focuses on econometric analysis. Comment citer ce document : Aubert, M., Debrune, O., Huat, J., Parrot, L. ( 2017). The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte. Presented at 11. Journées de Recherches en Sciences Sociales (JRSS), Lyon, FRA (2017-12-14 -2017-12-15) .

14 The model implemented let us appreciate that almost all factors influencing the farmers' behaviour are considered since the concordant rate of our model equals 82.16 % (Table 4).

Comment citer ce document : Aubert, M., Debrune, O., Huat, J., Parrot, L. ( 2017). The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte. Presented at 11. Journées de Recherches en Sciences Sociales (JRSS), Lyon, FRA (2017-12-14 -2017-12-15) .

15 Econometric results that identify brakes and leverages, at the farmer level thanks to the second survey, have to be put into perspective with the first qualitative survey (Table 4). This cross reading lets appreciate constraints refraining producers to promote their productive efforts in terms of environmental-friendly practices.

Results from the econometric model highlight that, in the Mayotte context, individual characteristics do not impact practices implemented (Hypothesis 1 non-validated). Neither the age nor the potential off-farm activity has an impact on the use of pesticides. This information is all the more important as it translates the importance of environmental factors.

Considering the physical dimension of the farm, estimated by the total workforce, our model underlines that farms that employ more workforce are more likely to implement environmental-friendly practices (Hypothesis 2 validated). This result translates that bigger farms benefit from economy of scale and a higher economic potential that let them reduce their chemical input used.

Comment citer ce document : Aubert, M., Debrune, O., Huat, J., Parrot, L. ( 2017). The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte. Presented at 11. Journées de Recherches en Sciences Sociales (JRSS), Lyon, FRA (2017-12-14 -2017-12-15) .

16

The financial dimension of the farm is considered through the access to European support. The results highlight the specificity of the Mahorais' context. As a matter of fact, the nonsignificance underlines that even if farmers can benefit from these supports, they are no more likely to implement environmental-friendly practice (Hypothesis 3 non-validated). To understand this point, let us highlight the experience of a farmer surveyed who benefited from support to buy a cistern. Even if this material was bought, the farmer could not use it since before being installed, it was stolen. The result confirms that in Mayotte, theft is a major problem (Agreste, 2011).

Results also confirm the importance of the location (Hypothesis 4 validated). Even if Mayotte is a small island, there are geographical specificities between the three main regions in terms of access to water, access to road and hence access to training. Mayotte is subjected to a water gradient (Figure 2). Southern farmer benefit from less water than those located in the north. Water is a major condition to tomatoes' productivity. Location also reflects roads and hence trainings access. As a matter of fact, training centres such as the agricultural high school in Coconi where are given every farming trainings are located in the centre of the island. Depending the location of the farmer, the access to these centres appears as a brake. Farmers located in the South are disadvantaged once more since sparsely served by paved roads.

Figure 2. Mayotte location specificities

Source: Météo France, 2017 -Geoportail

The hazard perception of farmers considered in our study appears to be non-relevant to understand the farmers' behaviour in terms of environmental-friendly practices (Hypothesis 5 non-validated). Even if farmers are conscious about the environmental impact of the pesticides used, the fact to be ill after consumption of contaminated fruits seems to be sufficient to modify their consumption's behaviour but not their farming practices.

Comment citer ce document : Aubert, M., Debrune, O., Huat, J., Parrot, L. ( 2017). The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte. Presented at 11. Journées de Recherches en Sciences Sociales (JRSS), Lyon, FRA (2017-12-14 -2017-12-15) .

17

The last hypothesis tested in our model is the importance to access to information (Hypothesis 6 validated). We observe that farmers who benefit from formal information are more likely to implement environmental-friendly practices rather than those who benefit from informal networks. During our investigations, almost all farmers underlined the need to be more supported by a technician for knowledge and skills acquisition and transfer. Even if they have access to some information through their official or non-official networks, their wish is to benefit from a concrete support of technician on their land. Almost all would like to implement environmental-friendly practices but they do not know the way to do. A long-term follow up is necessary for all farmers who need advise since between custom and belief, some farmers do not hesitate for instance to treat using ourouva, which is a toxic plant, or to use fire to avoid pests. Supervision and monitoring would help farmers to improve their productive practices.

Beyond results highlighted by the econometric model, the investigation of the first survey that considers all actors of the sector, we have observed two main brakes to help farmers implementing environmental-friendly practices.

At a financial level, farmers have to be supported at the very first stage since some of them neither read, nor write and speak French. During our investigation alongside producers, some confess not to benefit from European financial support, whereas they are eligible to, because of this language divide.

The second brake that is the main factor for the adoption of environmental-friendly practices is the lack of laboratories to perform phytosanitary tests. Since in Mayotte there is no laboratory, even if producers implement environmental-friendly practices, they cannot promote the quality of their production. Hence, neither farmers nor cooperatives can promote alternative practices. No collective action can be undertaken at this stage.

Conclusion

Mayotte is a French department since 2011 and an overseas department since 2014. Its recent integration of Mayotte to France and hence to European makes Mayotte a relevant case study. As a matter of fact, Mayotte has to answer phytosanitary requirements and harmonize farmers' practices with the legislation. Mayotte is also a relevant case study since legal and illegal population co-habites and since the agricultural legal population considers both formal and non-formal producers. While the first ones benefit from a SIRET number and hence can benefit from european support, the second ones have no right to produce and sell their production. Our study focuses hence on this first population. More precisely, our study considers the tomatoe's sector since it represents one of the main crop using pesticides.

Based on two surveys, our study aims both at appreciating the organisation of the tomatoe's sector and at understanding to what extend farmers are more likely to implement environmental-friendly practices. While the first survey considers almost all actor of the sector, the second one considers formal farmers. This last survey let us implement an Comment citer ce document : Aubert, M., Debrune, O., Huat, J., Parrot, L. ( 2017). The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte. Presented at 11. Journées de Recherches en Sciences Sociales (JRSS), Lyon, FRA (2017-12-14 -2017-12-15) .

18 econometric model to understand to what extend individual characteristics of farmers, structural and financial characteristics of their farm impact their pesticide use. More than these factors, our study also considers the location specificity and the impact of institutional environment through the access to formal or informal network.

The main results confirms the need for farmers to walk hand by hand with institutional supports. More precisely, while some support have to be defined at the producer level, others have to be identified at a more aggregated level.

At the producer level, financial support does not appear to be the first leverage. As a matter of fact, because of theft farmers cannot benefit from these supports. Robberies divert farmers from the use of such support since they are stolen before being installed. Moreover, even if farmers can benefit from financial support they are not necessarily able to ask them because of the language divide. Mahorais do not all speak and read French.

At an aggregated level, the first brake identified is the infrastructure. Three main regions can be defined. While some benefit from access to water and road, others are penalized. These lack go beyond the only infrastructure need since the non-accessibility of tracks prevent farmers to go and benefit from training. The infrastructure dimension appears also in terms of laboratory. There is indeed no laboratory in Mayotte to let farmers or organisation promote the quality of their production. None can confirm that practices implemented are more environmental-friendly and answer phytosanitary' requirement. In such context, no incitation to implement these practices appears to be relevant since none can control their effective implementation.

The implementation of environmental-friendly practices in Mayotte is still in its infancy. More than individual brakes, farmers suffer from institutional environment brakes. Because of the recent adhesion of Mayotte as a French department, numerous efforts are performed and time will let Mahorais' farmers improve their productive practices. The main limit to our study is due to the specific context of Mayotte. As a matter of fact, our study focuses on formal farmers but we have to notice that 80 % of the farmers are illegal or non-formal. The aim of our study is not only to understand the farmers' behaviour but also to identify leverages that could help the whole mahorais' agriculture to improve the quality of its production. Since only formal farmers can benefit from european support, we had to concentrate on this population. One perspective is hence to follow non-formal farmers and study to what extend they will be incitated to become formal, knowing that to become formal, farmers have to obtain a SIRET number proving they are mahorais and paying 21€.

Comment citer ce document : Aubert, M., Debrune, O., Huat, J., Parrot, L. ( 2017). The institutional environment as an essential support to agro ecology: the case of the formal market gardeners in Mayotte. Presented at 11. Journées de Recherches en Sciences Sociales (JRSS), Lyon, FRA (2017-12-14 -2017-12-15) .

Figure 1 .

 1 Figure 1. Determinants of the implementation of environmental-friendly practices

  4 1 hectare = 2.47 acres Comment citer ce document : Aubert, M., Debrune, O., Huat, J., Parrot, L. (

  . Its isolation, low area, small economy, hilly landscape and hard climate (two distinct season under a wet tropical climate) are recognized by the new European status (De Lavergne et al., 2012). It gives to Mayotte access to financial measures, and particularly concerning trade and fiscal policy for agriculture and fishing. For the agricultural sector, Mayotte must meet European requirements, with, in particular, the European framework directive 2009/128/CE, aiming at sustainably use phytosanitary product in every Member State. Through the French national plan Ecophyto, only operating since 2013 in Mayotte, a drastic change in production practices has emerged. The transition towards agroecological practices and alternative innovating methods to phytosanitary product is allocated by financial and technical European and national means. Food value chain structuration, upgrading farms, innovation and transfer project are carried by European and national programs as PDR 2 or POSEI 3 . They aim at enhancing Mayotte agricultural sector and at reducing its pesticide consumption.

Table 1 . Description of variables

 1

	Variable	Unit	Definition
		Interest variable
	pps	yes/no	Use of phytosanitary product
		Farmer's characteristics (H1)
	age	-	Age of the farmer
	off_farm_activity	yes/no	The farmer has an off-farm activity
		Farm's characteristics (H2)
	workforce	-	Number of workforce supporting the farm work
	horticulture_diversification	-	Number of horticulture products
		Financial dimension (H3)
	loan	yes/no	The farmer already asked for a loan to the bank
	financial_support	yes/no	The farmers has/had financial support from France or Europe
		Location (H4)
	location	(1) weast ; (2) east ; (3) south	Location of the farm
	water	yes/no	Water is easily accessible and available for farming
	Road	(0) bad (1) good	Quality of road to go to the farm
	slope	yes/no	More than 50% of the farm is on a slope
		Hazards perception (H5)
	background	yes/no	Health damaged enounced after tomato consumption
		Institutional environment (H4)
	referent	(0) Informal; (1) Formal	Technical referent

Table 2 . Quantitative characterisation of formal farmers depending they use, or not, pesticides

 2

		Pps	Mean	Equality of mean	Std Deviation	Equality of variance
		Farmers' characteristics (H1)
	age	No Yes	46,3 53	*	12,95 13,45	ns
		Farms' characteristics (H2)
	workforce	No Yes	1,91 2,89	***	1,05 1,08	ns
	horticulture_diversification	No yes	5,75 6,04	ns	2,62 2,82	ns

Table 3 . Qualitative characterisation of formal farmers depending they use, or not, pesticides

 3

			Repartition Use of pesticide no yes		Equality of distribution
		Farmers characteristics (H1)
	off_farm_activity	no yes	79% 21%	78% 22%	ns
		Financial dimension (H3)
	Loan	yes no	62% 38%	65% 35%	ns
	financial support	no yes	50% 50%	56% 44%	ns
			Location (H4)
		West	46%	35%
	Location	East	38%	35%	ns
		South	16%	29%
	Water	no yes	38% 62%	40% 60%	ns
	Road	Not paved Paved	42% 58%	35% 65%	ns
	Slope	no yes	71% 29%	79% 21%	ns
		Hazards perception (H5)
	Perception	no yes	38% 62%	53% 47%	ns
		Institutional environment (H6)
	Referent	informal institutional	75% 25%	65% 35%	ns

Table 4 . Econometric model

 4

		Coef.	Std. Err.	z	P>|z|	Odds Ratio
		Hypothesis 1: Individual characteristics
	Age	.0059019	.0349473	0.17	0.866
	Off farm activity	-.7086424	.9634848	-0.74	0.462	.4923121
		Hypothesis 2: Structural characteristics
	Workforce	1.3909***	.488455	2.85	0.004
	Specialization in tomato	.0359451	.0260401	1.38	0.167
	horticultural diversification .1249624	.1721143	0.73	0.468
	Expansion	1.116221	1.019156	1.10	0.273	3.053295
		Hypothesis 3: Financial characteristics
	Loan	-.5927116	1.047991	-0.57	0.572	.5528262
	Financial support	1.177423	1.132234	1.04	0.298	3.245999
		Hypothesis 4: Location
	Location			(Reference : West)
	East	.0148257	1.044913	0.01	0.989	1.014936
	South	2.145506*	1.275832	1.68	0.093	8.546362
		Hypothesis 5: Hazard perception
	Background	.150235	.903114	0.17	0.868	1.162107
		Hypothesis 6: Institutional environment
	Referent	1.702858*	1.032916	1.65	0.099	5.489615
	Constant	-6.843223	2.69473	-2.54	0.011
	Concordant Rate			82.61%

https://ec.europa.eu/agriculture/envir/cap_en

Rural Development Program


Michel Fliess

Cédric Join

Intelligent PID Controllers

Keywords: PID control, intelligent PID controllers, modelfree control, fast estimation techniques, numerical differentiation, linear systems, nonlinear systems, flatness-based control, delay systems

Intelligent PID controllers, or i-PID controllers, are PID controllers where the unknown parts of the plant, which might be highly nonlinear and/or time-varying, are taken into account without any modeling procedure. Our main tool is an online numerical differentiator, which is based on easily implementable fast estimation and identification techniques. Several numerical experiments demonstrate the efficiency of our method when compared to more classic PID regulators.

I. INTRODUCTION

Recent model-free control strategies have been proposed in [START_REF] Fliess | Complex continuous nonlinear systems: their black box identification and their control[END_REF] and [START_REF] Fliess | Vers une commande multivariable sans modèle, Actes Conf. Francoph. Automat. (CIFA-2006[END_REF]. They are based on new techniques for fast identification and estimation (see [START_REF] Fliess | Nonlinear estimation is easy[END_REF] and the references therein) and they have been shown to be quite efficient not only via academic examples in [START_REF] Fliess | Vers une commande multivariable sans modèle, Actes Conf. Francoph. Automat. (CIFA-2006[END_REF], [START_REF] Fliess | Complex continuous nonlinear systems: their black box identification and their control[END_REF] but also thanks to concrete case-studies1 in [START_REF] Gédouin | Model-free control of shape memory alloys antagonistic actuators[END_REF], [START_REF] Join | Étude préliminaire d'une commande sans modèle pour papillon de moteur[END_REF], [START_REF] Villagra | Robust stop-and-go control strategy: an algebraic approach for nonlinear estimation and control[END_REF].

This setting is based for a SISO system on the local description

y (n) = F + αu (1)
where α is some given constant. The function F = y (n)αu, which is obtained via an estimation of the n th -order derivative of the output signal, carries the whole information on the process we want to control: it might include severe nonlinearities as well as complex time-varying phenomena, like frictions. In all the examples we have investigated until now, we took n = 1 or n = 2. If n = 2, we obtained the desired behavior via the following intelligent PID controller 2 , or i-PID controller,

u = - F α + ÿ * α + K P e + K I e + K D ė (2)
where y * is a reference output trajectory, and e = y-y * . The aim of this communication is to show the superiority of those i-PID regulators with respect to more classic approaches of PID control. Our paper is organized as follows. Sect. II is devoted to a short review of model-free control and gives the definition of cedric.join@cran.uhp-nancy.fr i-PID controllers. It contains moreover the basic principles of our numerical differentiators. The three examples of Sect. III, with numerous convincing computer simulations, are

• a stable linear system, • an unstable nonlinear system, • a spring with unknown damping, friction and nonlinearity.

The conclusion in Sect. IV is stressing the benefits of our viewpoint for industrial control applications, and lists some open questions.

Remark 1: We are perfectly aware that such a comparison with existing techniques may be objected on the basis of the huge literature on PID controllers since the founding papers by Ziegler & Nichols [START_REF] Ziegler | Optimum settings for automatic controllers[END_REF], Cohen & Coon [START_REF] Cohen | Theoretical consideration of retarded control[END_REF], and Kessler [START_REF] Kessler | Das symmetrische Optimum[END_REF] (see, e.g., [START_REF] Alfaro | PID controllers'fragility[END_REF], [START_REF] Ang | PID control system analysis, design, and technology[END_REF], [START_REF] Aström | Advanced PID Control[END_REF], [START_REF] Besanc ¸on-Voda | Régulateurs PID analogiques et numériques[END_REF], [START_REF] Chen | Applying neural networks to online updated PID controllers for nonlinear process control[END_REF], [START_REF] Choi | PID Trajectory Tracking Control for Mechanical Systems[END_REF], [START_REF] Datta | Structure and Synthesis of PID Controllers[END_REF], [START_REF] Dieulesaint | Automatique appliquée -t. 1 : les procédés physiques de transformation[END_REF], [START_REF] Dindeleux | Technique de la regulation industrielle[END_REF], [START_REF] Flaus | La régulation industrielle[END_REF], [START_REF] Föllinger | Regelungstechnik -Einführung in die Methoden und ihre Anwendung[END_REF], [START_REF] Franklin | Feedback Control of Dynamic Systems[END_REF], [START_REF] Giöngy | On the automatic tuning and adaptation of PID controllers[END_REF], [START_REF] Johnson | PID Control: New Identification and Design Methods[END_REF], [START_REF] De Larminat | Automatique appliquée[END_REF], [START_REF] Lequesne | [END_REF], [START_REF] Lequin | Iterative feedback tuning of PID parameters: comparison with classical tuning rules[END_REF], [START_REF] Li | PID control system analysis and design[END_REF], [START_REF] Li | Hardware implementation of fuzzy PID controllers[END_REF], [START_REF] Longchamp | Commande numérique des systèmes dynamiques[END_REF], [START_REF] Morari | Robust Process Control[END_REF], [START_REF] O'dwyer | Handbook of PI and PID Controller Tuning Rules[END_REF], [START_REF] Pigeron | Boucles de régulation, 4 e éd[END_REF], [START_REF] Reznik | PID plus fuzzy controller structures as a design base for industrial applications[END_REF], [START_REF] Shinskey | Process Control Systems -Application, Design, and Tuning[END_REF], [START_REF] Silva | On the stability and controller robustness of some popular PID tuning rules[END_REF], [START_REF] Skogestad | Simple analytic rules for model reduction and PID controller tuning[END_REF], [START_REF] Vilanova | IMC based robust PID design: Tuning guidelines and automatic tuning[END_REF], [START_REF] Visioli | Practical PID Control[END_REF], [START_REF] Yu | Autotuning of PID Controllers[END_REF] and the references therein). It might always be argued that some already existing methodologies were ignored and/or misused. Only time and the combined effort of many control engineers will be able to establish our thesis on a completely firm basis.

II. I-PID CONTROLLERS

A. Model-free setting 31) General principles: Take a finite-dimensional SISO system E(t, y, ẏ, . . . , y (ι) , u, u, . . . , u (κ) ) = 0 which is linear or not, where E is a sufficiently smooth function of its arguments. Assume that for some integer n, 0 < n ≤ ι, ∂E ∂y (n) ≡ 0. The implicit function theorem yields then locally y (n) = E(t, y, ẏ, . . . , y (n-1) , y (n+1) , . . . , y (ι) , u, u, . . . , u (κ) )

By setting E = F + αu, we obtain Eq. ( 1) where

• α ∈ R is a non-physical constant parameter, which is
chosen by the engineer in such a way that F and αu are of the same magnitude,

• F is determined thanks to the knowledge of u, α, and of the estimate of y (n) .

Remark 2: A system might only be partially unknown as in Sect. III-C. It is straightforward to adapt the previous method to this case.

2) Numerical differentiation

4 : Start with a polynomial time function x N (t) = N ν=0 x (ν) (0) t ν ν! ∈ R[t],
t ≥ 0, of degree N . The usual notations of operational calculus (see, e.g., [START_REF] Yosida | Operational Calculus: A Theory of Hyperfunctions[END_REF]) yield X N (s) = N ν=0

x (ν) (0) s ν+1 . Multiply both sides by positive powers of the algebraic derivative d ds . The quantities x (ν) (0), ν = 0, 1, . . . , N , which are linearly identifiable, satisfy the following triangular system of linear equations:

d α s N+1 XN ds α = d α ds α N X ν=0 x (ν) (0)s N-ν ! 0 ≤ α ≤ N -1 (3)
Multiplying both sides of Eq. ( 3) by s -N , N > N , permits to get rid of time derivatives, i.e., of

s µ d ι XN ds ι , µ = 1, . . . , N , 0 ≤ ι ≤ N .
Consider now an analytic time function, defined by the power series

x(t) = ∞ ν=0 x (ν) (0) t ν ν! , which is assumed to be convergent around t = 0. Approximate x(t) by the truncated Taylor expansion x N (t) = N ν=0 x (ν) (0) t ν
ν! of order N . Good estimates of the derivatives are obtained by the same calculations as above.

3) Noise removal: Corrupting noises are viewed as highly fluctuating phenomena, which are attenuated via low pass filters (see [START_REF] Fliess | Analyse non standard du bruit[END_REF] for more details). Such filters may be obtained for instance by multiplying both sides of Eq. ( 3) by s -N , where N > 0 is large enough.

B. Controllers

If n = 2 in Eq. ( 1), the desired behavior is obtained via the intelligent PID controller, or i-PID controller, (2) where

• K P , K I , K D are the tuning parameters,
• y * is a reference output trajectory, • e = yy * is the output tracking error. Remark 3: If n = 1 in Eq. ( 1), replace Eq. ( 2) by the intelligent PI controller, or i-PI controller,

u = - F α + ẏ * α + K P e + K I e (4)
Remark 4: We were never obliged until now to choose n 2 in Eq. ( 1). If nevertheless this happens we would easily extend the generalized proportional-integral controllers, or GPI controllers, of [START_REF] Fliess | Correcteurs proportionnels-intégraux généralisés[END_REF] to intelligent generalized proportional-integral controllers, or i-GPI controllers.

Let us emphasize the following differences with respect to more classic approaches of PID controllers:

• No identification procedure is needed since the whole structural information is contained in the term F which is canceled. We are able to control high dimensional and/or strongly nonlinear systems without any complex and time-consuming parameter tuning.

• The flatness-based-like output reference trajectory (see, e.g., [START_REF] Fliess | Flatness and defect of non-linear systems: introductory theory and examples[END_REF], [START_REF] Sira-Ramírez | Differentially Flat Systems[END_REF]) is much more flexible than the step trajectory between two setpoints which still is quite common in industry. It permits to a large extent to avoid overshoots and undershoots.

III. COMPUTER SIMULATIONS AND COMPARISONS

All computer simulations are performed with a corrupting additive white Gaussian noise, which is zero-mean and with variance 0.01. With classic PID regulators standard low-pass filters are utilized whereas robustness with respect to noises for i-PID controllers is ensured via the principles of Sect. II-A.3.

A. A stable linear system

The transfer function

(s + 2) 2 (s + 1) 3 (5)
defines a stable linear system. 1) A classic PID controller: We follow Dindeleux [START_REF] Dindeleux | Technique de la regulation industrielle[END_REF] and apply Broïda's method by approximating the inputoutput behavior (5) by the delay system

Ke -τ s (T s + 1)
The parameters K, T , τ are obtained via graphical methods: K = 4, T = 2.018, τ = 0.2424. It yields the following PID coefficients: 3) Simulation results: Fig. 1 shows that our i-PI controller behaves slightly better than the classic PID regulator. The situation is much more revealing if we assume that

K P = 100(0.4τ +T ) 120Kτ = 1.8181, K I = 1 1.33Kτ = 0.7754, K D = 0.35T K = 0.
• our system is changing with time, • a fault is occurring. The system poles are no more located at 1 but at 1.5, i.e., its transfer function becomes

(s + 2) 2 (s + 1.5) 3
Fig. 2 demonstrates that the difference between our i-PI controller becomes quite important with the classic PID regulator if we do not perform again the graphical identification techniques.

The actuator failure in Fig. 3 is a 50% power loss. Here again our i-PI controller behaves much better than the standard PID controller.

B. An unstable nonlinear system

Consider the unstable nonlinear system 6) via the delay system

ẏ -y = u 3 (6)
Ke -τ s s (7)
The parameters K, τ are again obtained via a graphical method around the operating point u = 1, y = 1.5: K = 2, τ = 0.2. It yields according to [START_REF] Dindeleux | Technique de la regulation industrielle[END_REF] the PID coefficients: K p = 100 110Kτ = 2.2727, K i = 1 6.66Kτ 2 = 1.8769 and K d = 0.35 K = 0.175. Remark 5: The quality of the above parameters strongly depends on the accuracy of the identification by Eq. ( 7). This identification here is quite "subtle", i.e., not very natural.

2) The i-PI controller: The coefficients K P and K I in Eq. ( 4) are selected in such that -2 is the double pole of the closed loop dynamics.

3) Simulation results: Fig. 4 shows the poor performances of the classic PID control with steps as reference trajectories. Note that for the numerical simulations we utilized for the PID controller, as often in industry, only the derivative of the output variable y:

u = K P ([y] e -y ⋆ ) + K I (y -y ⋆ ) + K D [ ẏ] e
Replace, following the principles of flatness-based control, the step reference trajectories by suitable smooth trajectories, which are defined here via Bézier polynomials. Even if the performance of the classic PID regulator increases, Figs. 5 and 6 demonstrate that the i-PI controller behaves much better.

4) Anti-windup: Set, for instance, -2 ≤ u ≤ 0.4. According to Fig. 7 we obtain second-rate performances without anti-windup (see, e.g., [START_REF] Hippe | Windup in Control -Its Effects and Their Prevention[END_REF]). With an anti-windup on the classical part of the i-PI controller, Fig. 8 shows that the reference trajectory should be modified according to the principles of flatness-based control.

C. An example of a partially known system

Consider the following spring

mÿ = -K(y) + F ( ẏ) -d ẏ + F ext ( 8
)
where y is the position of a point mass m, F ext = u is the control, d is the damping, K(y) = k 1 y + k 3 y 3 contains a cubic Duffing nonlinearity, F ( ẏ) is the friction. The mass m = 0.5 is perfectly known. The error on the coefficient k 1 = 5 is 40% since we are utilizing the value k1 = 3 in the simulations. The true values of the coefficients d and k 3 , which are unknown, are 1 and 2 in the simulations. controllers depends on practical implementation issues, like the quality of the sensors, the magnitude of the corrupting noises, the sampling period, and the computer capability.

A more detailed presentation will appear in [START_REF] Fliess | Commande sans modèle et commande à modèle restreint[END_REF], where some important questions, like multivariable systems, and non-minimum phase systems, will also be examined.

  1766. 2) The i-PI controller: The very simple model ẏ = F + u is used. Write [•] e the estimate of a given quantity. Introduce the i-PI controller u = -[F ] e + ẏ⋆ + PI(e) where • [F ] e = [ ẏ] eu, • y ⋆ is a reference trajectory, • e = yy ⋆ , • PI(e) is a standard PI controller.

Fig. 2 .Fig. 3 .

 23 Fig. 1. Stable linear system

Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .

 45678 Fig.[START_REF] Aström | Towards intelligent PID control[END_REF]. PID control for the unstable nonlinear system with steps as reference trajectory

Fig. 9 .

 9 Fig. 9. Spring with unknown nonlinearity, friction, and damping

Some industrial implementations, which will be discussed elsewhere, are already being developed.

This terminology has already been used by other authors (see, e.g.,[START_REF] Aström | Towards intelligent PID control[END_REF]), but with a quite different meaning.

See[START_REF] Fliess | Complex continuous nonlinear systems: their black box identification and their control[END_REF] and[START_REF] Fliess | Vers une commande multivariable sans modèle, Actes Conf. Francoph. Automat. (CIFA-2006[END_REF] for more details.

See[START_REF] Mboup | A revised look at numerical differentiation with an application to nonlinear feedback control[END_REF] for the most recent and powerful advances. The reference[START_REF] Fliess | Nonlinear estimation is easy[END_REF] contains a quite extensive bibliography on this subject.

Tribology is a most difficult domain which is still attracting a lot of studies (see, e.g.,[START_REF] Nuninger | Bilan et enjeux des modèles de frottements: tribologie et contrôle au service de la sécurité des transports[END_REF],[START_REF] Olsson | Friction models and friction compensation[END_REF], and the references therein). Let us stress here that we do not need here any modeling of frictions.

Acknowledgements. The authors would like to thank Dr. O. Gibaru (INRIA-ALIEN -École des Arts & Métiers ParisTech, Lille) for some helpful discussions.

Choose for the friction 5 in the numerical simulations the classic Tustin model [START_REF] Tustin | The effect of backlash and speed-dependent friction on the stability of closed-cycle control systems[END_REF]: Fig. 9-(a) shows a quite "brutal" behavior when the sign of the speed is changing.

1) A classic PID controller: We design a PID controller with respect to the partially known model mÿ = -k1 y + u. Its coefficients are selected such that all closed loop poles are equal to -3:

2) The i-PID controller: Select a reference trajectory y ⋆ . Set u ⋆ = mÿ ⋆ + k1 y ⋆ . The designed control is

where

which is bringing together all the complex and poorly known phenomena (damping, friction, nonlinearity), is estimated via

which is deduced from Eq. ( 8).

• The i-PID controller PID(e), e = yy ⋆ , is chosen such that -3 is the only pole. 3) Simulation results: Fig. 9-(c,d) demonstrate excellent results for the control [START_REF] Datta | Structure and Synthesis of PID Controllers[END_REF], when compared to those in • Fig. 9-(e,f) with a flatness-based nominal trajectory and a classic PID controller, but without taking into account the unknown effects,

• Fig. 9-(g,h) with a classic PID controller, but without a flatness-based nominal trajectory and without taking into account the unknown effects. When the friction is becoming more important, the tracking performances without estimating G are deteriorating whereas those of the i-PID controller (9) are unaltered.

IV. CONCLUSION

The first two examples seem to show that delay systems defined by transfer functions of the form T (s)e -Ls , T ∈ R(s), L ≥ 0, which play since Ziegler & Nichols [START_REF] Ziegler | Optimum settings for automatic controllers[END_REF] such a fundamental role in the parameter tuning of PID controllers, might loose their importance. See [START_REF] Fliess | An extension of predictive control, PID regulators and Smith predictors to some delay systems[END_REF] for a general study of this class of systems.

Consider the following problems with classic PID regulators:

• How to ensure good performances with disparate plants without having to tune again and again the PID parameters?

• How to guarantee a suitable adaptation when the plant is changing with time? Our intelligent PID controllers offer a most efficient answer to those crucial points for any industrial application, which is moreover easily implementable: F in Eq. ( 1) is estimated online.

The first example in Sect. III-A demonstrates that the familiar mathematical robustness criteria are becoming pointless here. It should be clear that the robustness of our i-PID