Les systèmes à commutations constituent un cas particulier des systèmes dynamiques hybrides. Ils sont composés d'une famille de systèmes et d'une loi de commutation qui détermine quel mode est activé à chaque instant. Ces systèmes représentent une large gamme de systèmes concrets. L'étude de la stabilité de ceux-ci a déjà été longuement abordée. Les travaux de cette thèse portent sur l'analyse de performance des systèmes à commutations linéaires en temps discret et sur la synthèse de différentes lois de commande pour ces systèmes en tenant compte de contraintes de performances. L'analyse de stabilité de ces systèmes a été étendue pour tenir compte de l'aspect performance qui a été modélisée par un critère quadratique. La valeur du critère dépendant des commutations, l'analyse porte sur le coût garanti des performances. Grâce à la résolution d'un problème d'optimisation sous des contraintes sous la forme d'inégalités matricielles linéaires, un majorant du coût garanti est déterminé. Une approche est proposée pour évaluer la qualité du majorant trouvé. Un deuxième point abordé est la conception de contrôleurs qui tiennent compte de l'aspect performance. Des méthodes de synthèse de différents contrôleurs (retour d'état, retour d'état reconstruit par observateur et retour de sortie dynamique) sont proposées dans ce cadre. Enfin, nos résultats ont été appliqués au cas des systèmes contrôlés en réseau. / Switched systems are a specific case of dynamical hybrid systems. They are made up of a family of subsystems and of a switching law which defines the activated subsystem at each instant. These systems depict a wide range of real systems. Stability's study has been intensely studied. This Ph.D. thesis deals with performance analysis for discrete-time switched linear systems and synthesis of different control laws by taking into account performance constraints. Stability's analysis for these systems was spread in order to taking into account performance aspect, modeled by a quadratic criterion. As the value of the criterion depends on commutations, the analysis is done for the guaranteed cost of performances. By solving an optimization problem under constraints in the form of linear matrices inequalities, an upper bound of the guaranteed cost is found. An approach is proposed to certificate the upper bound. An other tackled point is the synthesis of controllers which take into account performance aspect. Methods of synthesis of different controllers (state feedback, state feedback based on observer and dynamic output feedback) are proposed. Last, our results are applied to networked controlled systems

Cette thèse se situe dans le cadre de l’analyse et de la synthèse des systèmes périodiques. Les contributions présentées dans ce mémoire portent sur la commande sous contraintes des systèmes linéaires discrets périodiques. Ces contraintes, portant sur l’état du système et/ ou sur la commande, peuvent être des contraintes de positivité ou de bornitude. Dans ce travail, des conditions d’analyse en stabilité et positivité des systèmes périodiques en termes de LMI (Inégalité Matricielle Linéaire) strictes, sont présentées. Ces outils d’analyse ont ensuite permis d’élaborer une loi de commande par retour d’état périodique. Les résultats obtenus sont exploités par la suite pour développer une commande par retour d’état périodique robuste pour les systèmes périodiques incertains. Des conditions de stabilisation robuste sont élaborées en utilisant la S-procédure. En outre, des conditions de stabilité et stabilisation par retour d’état périodique des systèmes périodiques avec retards sont établies. Le problème de stabilisation de ce type de systèmes sous un certain nombre de contraintes est résolu en suivant deux approches, la première est basée sur les techniques de Lyapunov la seconde fait appel à la programmation linéaire. Outre la notion de stabilité, la notion de performance des systèmes en boucle fermée est traitée. Pour cela, nous proposons une commande de type H∞ pour résoudre le problème de rejet de perturbations. / This thesis deals with the analysis and the control problem of periodic linear discrete systems (PLDS). The contributions presented in this work focuses on the constrained control of PLDS. Conditions for stability analysis and positivity are established in terms of strict LMI (Linear Matrix Inequalities). The stabilization of PLDS under the condition that the closed-loop system is positive and stable is addressed as well as the case of bounded state and/ or control variables. The obtained results are then extended to the synthesis of robust state feedback controllers, where some of which are based on the S − procedure technique. Furthermore, some conditions of stability and stabilization of PLDS with delays are established. The problem of stabilization of constrained PLDS is addressed based on the Lyapunov techniques or the Linear Programming techniques. The robust H∞ state feedback control in which both robust stability and a prescribed H∞ performance are required is investigated.

Esta tese aborda o problema de regulação para sistemas lineares sujeitos a saltos Markovianos de tempo discreto com matrizes de transição incertas. Considera-se que as incertezas são limitadas em norma e os estados da cadeia de Markov podem não ser completamente observados pelo controlador. No cenário com observação completa dos estados, a solução é deduzida com base em um funcional quadrático dado em termos das probabilidades de transição incertas. Enquanto que no cenário sem observação, a solução é obtida por meio da reformulação do sistema Markoviano como um sistema determinístico, independente da cadeia de Markov. Três modelos são propostos para essa reformulação: um modelo é baseado no primeiro momento do sistema Markoviano, o segundo é obtido a partir da medida de Dirac e resulta em um sistema aumentado, e o terceiro fornece um sistema aumentado singular. Os reguladores recursivos robustos são projetados a partir de critérios de custo quadrático, dados em termos de problemas de otimização restritos. A solução é derivada da técnica de mínimos quadrados regularizados robustos e apresentada em uma estrutura matricial. A recursividade é estabelecida por equações de Riccati, que se assemelham às soluções dos reguladores clássicos, para essa classe de sistemas, quando não estão sujeitos a incertezas. / This thesis deals with regulation problem for discrete-time Markovian jump linear systems with uncertain transition matrix. The uncertainties are assumed to be normbounded type. The states of the Markov chain can not be completely observed by the controller. In the scenario with complete observation of the states, the solution is deduced based on a quadratic functional given in terms of uncertain transition probabilities. While in the scenario without observation, the solution is obtained from reformulation of the Markovian system as a deterministic system, independent of the Markov chain. Three models are proposed for the reformulation process: a model is based on the first moment of the Markovian system, the second is obtained from Dirac measure which results in an augmented system, and the third provides a singular augmented system. Recursive robust regulators are designed from quadratic cost criteria given in terms of constrained optimization problems. The solution is derived from the robust regularized least-square approach, whose framework is given in terms of a matrix structure. The recursiveness is established by Riccati equations which resemble the solutions of standard regulators for this class of systems, when they are not subject to uncertainties.

In telecommunications, distributed cooperative communications refer to techniques which allow different users in a wireless network to share or combine their information in order to increase diversity gain or power gain. Unlike conventional point-to-point communications maximizing the performance of the individual link, distributed cooperative communications enable multiple users to collaborate with each other to achieve an overall improvement in performance, e.g., improved range and data rates. The first part of this dissertation focuses the problem of jointly decoding binary messages from a single distant transmitter to a cooperative receive cluster. The outage probability of distributed reception with binary hard decision exchanges is compared with the outage probability of ideal receive beamforming with unquantized observation exchanges. Low- dimensional analysis and numerical results show, via two simple but surprisingly good approximations, that the outage probability performance of distributed reception with hard decision exchanges is well-predicted by the SNR of ideal receive beamforming after subtracting a hard decision penalty of slightly less than 2 dB. These results, developed in non-asymptotic regimes, are consistent with prior asymptotic results (for a large number of nodes and low per-node SNR) on hard decisions in binary communication systems. We next consider the problem of estimating and tracking channels in a distributed transmission system with multiple transmitters and multiple receivers. In order to track and predict the effective channel between each transmit node and each receive node to facilitate coherent transmission, a linear time-invariant state- space model is developed and is shown to be observable but nonstabilizable. To quantify the steady-state performance of a Kalman filter channel tracker, two methods are developed to efficiently compute the steady-state prediction covariance. An asymptotic analysis is also presented for the homogenous oscillator case for systems with a large number of transmit and receive nodes with closed-form results for all of the elements in the asymptotic prediction covariance as a function of the carrier frequency, oscillator parameters, and channel measurement period. Numeric results confirm the analysis and demonstrate the effect of the oscillator parameters on the ability of the distributed transmission system to achieve coherent transmission. In recent years, the development of efficient radio frequency (RF) radiation wireless power transfer (WPT) systems has become an active research area, motivated by the widespread use of low-power devices that can be charged wirelessly. In this dissertation, we next consider a time division multiple access scenario where a wireless access point transmits to a group of users which harvest the energy and then use this energy to transmit back to the access point. Past approaches have found the optimal time allocation to maximize sum throughput under the assumption that the users must use all of their harvested power in each block of the "harvest-then-transmit" protocol. This dissertation considers optimal time and energy allocation to maximize the sum throughput for the case when the nodes can save energy for later blocks. To maximize the sum throughput over a finite horizon, the initial optimization problem is separated into two sub-problems and finally can be formulated into a standard box- constrained optimization problem, which can be solved efficiently. A tight upper bound is derived by relaxing the energy harvesting causality. A disadvantage of RF-radiation based WPT is that path loss effects can significantly reduce the amount of power received by energy harvesting devices. To overcome this problem, recent investigations have considered the use of distributed transmit beamforming (DTB) in wireless communication systems where two or more individual transmit nodes pool their antenna resources to emulate a virtual antenna array. In order to take the advantages of the DTB in the WPT, in this dissertation, we study the optimization of the feedback rate to maximize the energy efficiency in the WPT system. Since periodic feedback improves the beamforming gain but requires the receivers to expend energy, there is a fundamental tradeoff between the feedback period and the efficiency of the WPT system. We develop a new model to combine WPT and DTB and explicitly account for independent oscillator dynamics and the cost of feedback energy from the receive nodes. We then formulate a "Normalized Weighted Mean Energy Harvesting Rate" (NWMEHR) maximization problem to select the feedback period to maximize the weighted averaged amount of net energy harvested by the receive nodes per unit of time as a function of the oscillator parameters. We develop an explicit method to numerically calculate the globally optimal feedback period.

Esta tese aborda o problema de regulação para sistemas lineares sujeitos a saltos Markovianos de tempo discreto com matrizes de transição incertas. Considera-se que as incertezas são limitadas em norma e os estados da cadeia de Markov podem não ser completamente observados pelo controlador. No cenário com observação completa dos estados, a solução é deduzida com base em um funcional quadrático dado em termos das probabilidades de transição incertas. Enquanto que no cenário sem observação, a solução é obtida por meio da reformulação do sistema Markoviano como um sistema determinístico, independente da cadeia de Markov. Três modelos são propostos para essa reformulação: um modelo é baseado no primeiro momento do sistema Markoviano, o segundo é obtido a partir da medida de Dirac e resulta em um sistema aumentado, e o terceiro fornece um sistema aumentado singular. Os reguladores recursivos robustos são projetados a partir de critérios de custo quadrático, dados em termos de problemas de otimização restritos. A solução é derivada da técnica de mínimos quadrados regularizados robustos e apresentada em uma estrutura matricial. A recursividade é estabelecida por equações de Riccati, que se assemelham às soluções dos reguladores clássicos, para essa classe de sistemas, quando não estão sujeitos a incertezas. / This thesis deals with regulation problem for discrete-time Markovian jump linear systems with uncertain transition matrix. The uncertainties are assumed to be normbounded type. The states of the Markov chain can not be completely observed by the controller. In the scenario with complete observation of the states, the solution is deduced based on a quadratic functional given in terms of uncertain transition probabilities. While in the scenario without observation, the solution is obtained from reformulation of the Markovian system as a deterministic system, independent of the Markov chain. Three models are proposed for the reformulation process: a model is based on the first moment of the Markovian system, the second is obtained from Dirac measure which results in an augmented system, and the third provides a singular augmented system. Recursive robust regulators are designed from quadratic cost criteria given in terms of constrained optimization problems. The solution is derived from the robust regularized least-square approach, whose framework is given in terms of a matrix structure. The recursiveness is established by Riccati equations which resemble the solutions of standard regulators for this class of systems, when they are not subject to uncertainties.

In this thesis different control methods are applied to the beam and ball system. Test setup for the previous thesis is handled, circuit assemblies and hardware redesigned. As the system is controlled by the control law partitioning method by a computer, discrete time system model is created. The controllability and the observability of the system are analyzed and a nonlinear controller by using control law partitioning in other words computed torque is designed. State feedback control algorithm previously designed is repeated. In case of calculating the non measurable state variables two different reduced order observers are designed for these two different controllers, one for control law partitioning controller and the other for state-feedback controller. Two controller methods designed for the thesis study are tested in the computer environment using modeling and simulation tools (Also a different controller by using sliding mode controller is designed and tested in the computer environment using simulation tools). A controller software program is written for the designed controller algorithms and this software is tested on the test setup. It is observed that the system is stable when we apply either of the control algorithms.

In this thesis study, a valveless hydraulic servo system controlled by two pumps is investigated and its performance characteristics are compared with a conventional valve controlled system both experimentally and analytically. The two control techniques are applied on the position control of a single rod linear actuator. In the valve controlled system, the flow rate through the actuator is regulated with a servovalve / whereas in the pump controlled system, two variable speed pumps driven by servomotors regulate the flow rate according to the needs of the system, thus eliminating the valve losses. To understand the dynamic behaviors of two systems, the order of the differential equations defining the system dynamics of the both systems are reduced by using the fact that the dynamic pressure changes in the hydraulic cylinder chambers become linearly dependent on leakage coefficients and cylinder chamber volumes above and below some prescribed cut off frequencies. Thus the open loop speed response of the pump controlled and valve controlled systems are defined by v second order transfer functions. The two systems are modeled in MATLAB Simulink environment and the assumptions are validated. For the position control of the single rod hydraulic actuator, a linear state feedback control scheme is applied. Its state feedback gains are determined by using the linear and linearized reduced order dynamic system equations. A linear Kalman filter for pump controlled system and an unscented Kalman filter for valve controlled system are designed for estimation and filtering purposes. The dynamic performances of both systems are investigated on an experimental test set up developed by conducting open loop and closed loop frequency response and step response tests. MATLAB Real Time Windows Target (RTWT) module is used in the tests for application purposes.

Η μερική διαφορική εξίσωση Hamilton-Jacobi-Bellman παράγει τη λύση στο πρόβλημα του υπολογισμού της βέλτιστης ανάδρασης καταστάσεων σε μη γραμμικά δυναμικά συστήματα. Η προσπάθεια ανάπτυξης εύχρηστων και αξιόπιστων μεθόδων αριθμητικής ή προσεγγιστικής επίλυσης της εξίσωσης Hamilton-Jacobi-Bellman έχει τεράστια σημασία στη ρύθμιση διεργασιών γιατί μπορεί να οδηγήσει άμεσα σε εργαλεία σχεδιασμού μη γραμμικών ρυθμιστών. Ειδικότερα, στη ρύθμιση διεργασιών, η απόδοση ενός ρυθμιστικού συστήματος αξιολογείται βάσει ενός τετραγωνικού δείκτη απόδοσης σε άπειρο χρονικό ορίζοντα, και η βέλτιστη ανάδραση καταστάσεων μπορεί να υπολογισθεί μέσω της λύσης της εξίσωσης Hamilton-Jacobi-Bellman, μη εξαρτώμενης από το χρόνο. Στο πρόβλημα της επίλυσης της παραπάνω εξίσωσης παρουσιάζονται σοβαρές δυσκολίες, κυρίως λόγω υπολογιστικής πολυπλοκότητας. Για το λόγο αυτό, οι μέχρι στιγμής πρακτικές εφαρμογές υπήρξαν περιορισμένες. Στην παρούσα εργασία αναπτύσσεται υπολογιστική μέθοδος, βασισμένη στον αλγόριθμο επαναλήψεων Newton-Kantorovich, η οποία επιτυγχάνει πολυωνυμική προσέγγιση της λύσης της μερικής διαφορικής εξίσωσης Hamilton-Jacobi-Bellman υπό μορφή αναπτύγματος σε δυναμοσειρά Taylor. Με τον τρόπο αυτό επιταχύνονται σημαντικά οι υπολογισμοί για τον προσδιορισμό της βέλτιστης ανάδρασης καταστάσεων. Η μέθοδος εφαρμόζεται αρχικά σε ένα παράδειγμα ισοθερμοκρασιακού αντιδραστήρα συνεχούς λειτουργίας με ανάδευση, ο οποίος παρουσιάζει δυναμική συμπεριφορά μη-ελάχιστης φάσης, με μία είσοδο, μία έξοδο και δύο καταστάσεις. Στη συνέχεια, εφαρμόζεται σε παραδείγματα μη ισοθερμοκρασιακού αντιδραστήρα αντίστοιχης δυναμικής συμπεριφοράς, τριών καταστάσεων, πρωτίστως με μία είσοδο και μία έξοδο και κατόπιν με δύο εισόδους και δύο εξόδους. Με ανάπτυξη και εφαρμογή κώδικα MAPLE για κάθε μία περίπτωση χωριστά, υπολογίζονται προσεγγιστικά οι βέλτιστοι νόμοι ανάδρασης και σχεδιάζονται οι βέλτιστες αποκρίσεις των εισόδων και των εξόδων κάθε ενός από τα παραπάνω συστήματα, ενώ ταυτόχρονα γίνεται και καταγραφή των αντίστοιχων χρόνων εκτέλεσης κάθε κώδικα. Τέλος, στην περίπτωση του ισοθερμοκρασιακού αντιδραστήρα, γίνεται σύγκριση της προτεινόμενης μεθόδου με προϋπάρχουσες, κατά κύριο λόγο σε ζητήματα χρόνων εκτέλεσης, αλλά και σε ζητήματα απόδοσης στη ρύθμιση. / The partial differential equation Hamilton-Jacobi-Bellman produces the solution in the problem of calculation of optimal state feedback in non-linear dynamic systems. The effort of designing functional and reliable, numerical or approximate, methods for solving Hamilton-Jacobi-Bellman equation has enormous importance in process control because it can lead directly to tools of planning non-linear regulators. More specifically, in process control, the attribution of a regulating system is evaluated using a quadratic performance index in infinite time horizon, and the optimal state feedback can be calculated by the solution of the non time depended Hamilton-Jacobi-Bellman equation. The problem of solving the equation above encounters serious difficulties, mainly because of the calculation complexity. For this reason, the practical applications existed until now were very few. In the present work a calculating method is developed, based in the iterative algorithm Newton-Kantorovich, which achieves polynomial approach of the solution of partial differential equation Hamilton-Jacobi-Bellman under the form of Taylor series expansion. Thus the calculations for the determination of optimal state feedback are considerably accelerated. The method is initially applied in an example of continuous stirred tank reactor, with non-minimum phase dynamic behavior, with one input, one output and two state variables. Afterwards, it is applied in examples of not isothermal reactor of the same dynamic behavior, three state variables, firstly with one input and one output variables and then with two input and two output variables. Using the symbolic program MAPLE, a code was developed for each case separately, which calculates approximately the optimal feedback laws and designs the optimal responses of the inputs and outputs of each of the systems above, while the corresponding times of implementation of each code are simultaneously recording. Finally, in the case of isothermal reactor, a comparison is made between the proposed and preexisting methods, mainly in the base of the time of implementations and the regulation performance.

Dans un contexte de réduction des émissions de CO2 dans les systèmes industriels et d’amélioration de leur efficacité énergétique, les chauffages par induction répondent à ces critères. Le procédé consiste à plonger un corps conducteur d’électricité dans un champ magnétique variable, induisant ainsi des courants au sein de la pièce qui se met alors à chauffer par effet Joule. Cette technologie présente l’avantage d’atteindre des températures élevées de manière précise et rapide, sans contact avec la source d’énergie. Si aujourd’hui le contrôle de tels procédés passe par la structure mécanique du chauffage, de nombreuses études ont montré que l’association de plusieurs bobines alimentées par des systèmes d’électronique de puissance fournit une souplesse dans le contrôle des profils de température et une flexibilité vis-à-vis des pièces traitées. Ce travail présente deux systèmes de chauffage par induction. Le premier est un prototype réalisé par EDF considérant trois inducteurs alimentés par trois onduleurs à résonance. Nous nous y intéresserons plus particulièrement par la suite. Le second, en cours de réalisation, met en jeu six inducteurs pour du chauffage au défilé. Leurs caractéristiques, leurs alimentations et leurs fonctionnements sont abordés pour ensuite mettre en place deux modélisations des phénomènes électriques, l’une sous forme de fonctions de transfert, la seconde dans l’espace d’état. L’objectif final est le développement d’une alimentation auto-adaptative capable de contrôler en temps réel le profil de puissance injecté dans les pièces à chauffer afin d’atteindre un profil de température requis avec le minimum d’énergie consommée. L’étude se poursuit avec un inventaire des solutions existantes en termes de commande en boucle ouverte et en boucle fermée des systèmes mono-inducteurs, ainsi que des travaux, plus rares, pour les chauffages multi-inducteurs. De plus, des études ont montré que le contrôle de la température à la surface d’une pièce à chauffer passait par le contrôle des courants dans les inducteurs, en amplitude mais également en phase. C’est pourquoi nous proposons des lois de commande pour asservir les courants dans les inducteurs. Une routine d’optimisation fournit les amplitudes et les phases des courants dans les trois inducteurs permettant d’obtenir le profil de température le plus proche d’un profil de référence. Nous l’avons modifiée de façon à tenir compte de solutions énergétiquement optimisées en intégrant les pertes dans les interrupteurs et les inducteurs. Deux lois de commande originales sont proposées. La première étudie une commande robuste dans l’espace d’état par placement de vecteurs propres. La seconde met en jeu des correcteurs résonants qui confèrent à la boucle du système un module de gain infiniment grand à la fréquence de résonance de sorte qu’ils effacent les effets des perturbations agissant à cette même fréquence. Les méthodes de synthèse de ces correcteurs sont échantillonnées avec un très faible rapport fréquence d’échantillonnage/fréquence de résonance ; les performances sont détaillées et analysées pour le prototype à trois inducteurs. Pour tester plus facilement et valider en partie les lois mises en place, un simulateur analogique a été conçu, sorte d’émulateur reproduisant le comportement des courants dans les inducteurs et des tensions à leurs bornes. Il se base sur la modélisation sous forme de fonctions de transfert et ne comprend donc pas d’onduleur. Par l’intermédiaire d’une carte dSPACE intégrant un DSP, nous avons implanté et validé les deux lois de commande robustes sur le simulateur analogique. Par la suite, pour se rapprocher du système réel, nous avons mis en place une commande rapprochée transformant les trois signaux de commande en sortie des correcteurs vers les rapports cycliques des douze interrupteurs des convertisseurs alimentant les inducteurs. Cette étape a été validée par des essais expérimentaux réalisés en parallèle de nos études. / In the context of reducing carbon dioxide emissions in industrial systems and improving their energy efficiency, induction heaters meet these criteria. The method consists in immersing an electrically conductive body in a variable magnetic field, inducing currents within the piece which then begins to heat by Joule effect. This technology has the advantage of reaching high temperatures accurately and quickly, without contact with the power source. Today the control of such works with mechanical structures. But many studies have shown that the combination of several coils supplied by electronic power systems provides flexibility in controlling temperature profiles and flexibility towards the treated parts. This paper presents two systems of induction heating. The first is a prototype made by EDF considering three inductors supplied by three resonant inverters. We will focus more specifically later on this prototype. The second one, in progress, involves six inductors for scrolling heating. Their characteristics, their power supplies and their functions are discussed and then set up two models of electric phenomena, one form of transfer functions and one form in the state space. The final objective is the development of a self-adaptive power able to control real-time power profile injected into parts of heating to achieve a temperature profile required with minimum energy consumption. The study goes on with a list of existing solutions in terms of open-loop control and closed-loop control for single inductor system, as well as few rarer works for multi-inductors heaters. In addition, studies have shown that control of the surface temperature of the piece to be heated passes by the control of currents in the inductors, in magnitude but also in phase. That is why we propose control laws for controlling inductor currents. An optimization routine provides the magnitudes and phases of the currents in the three inductors to obtain the temperature profile closer to a reference profile. We modified it to take into account energy optimized solutions by integrating the losses in the switches and inductors. Two original control laws are proposed. The first one studies a robust control in the state space by placing eigenvalues and eigenvectors. The second one involves resonant markers that give the system loop gain module infinitely large at the resonant frequency so that they erase the effects of disturbances acting at the same frequency. The methods of synthesis of these markers are sampled with a very low sampling frequency / resonant frequency ratio; performance are detailed and analyzed for the prototype with three inductors. So as to test and validate easily some of the studied laws, an analog simulator was designed, a kind of an emulator, which reproduces the behaviour of the currents in the coils and the voltages at their terminals. It is based on the transfer function model and therefore does not include inverters. Through a dSPACE card integrating a DSP, we have implemented and validated the two robust control laws on the analog simulator. Thereafter, in order to be closer to the real system, we have established a close control which turns the three control signals toward the duty cycles of the twelve switches of the converters supplying the inductors. This step was validated by experimental tests carried out in parallel with our studies.

L’objectif de ce travail de thèse est de démontrer pour la première fois la capture, la manipulationet la caractérisation de molécules biologiques grâce à une micropince réaliséeen technologie microsystème. La molécule d’ADN étant, dans un premier temps, la moléculecible, des fibres d’ADN sont capturées grâce à l’immersion de la micropince dansun petit volume inférieur à 1 μL de solution contenant les molécules. Elles sont ensuitecaractérisées mécaniquement et électriquement grâce aux fonctionnalités intégrées sur lamême puce en silicium.Le second volet de ce travail consiste à améliorer les performances du système pouratteindre la résolution d’une seule molécule. En effet dans le but d’étudier les phénomènesd’interactions au niveau moléculaire, il s’avère essentiel d’améliorer le système. Dans cebut précis, une commande par retour d’état de la micropince est étudiée. Elle permetalors de spécifiquement sensibiliser le système aux variations de raideur mécanique dusystème {micropince + molécules d’ADN}.[...] / The main objective of this Ph.D. work is to achieve biological experimentson DNA molecules with versatile silicon nanotweezers. Experiments on single moleculerely mostly on Optical Tweezers, Magnetic Tweezers or Atomic Force Spectroscopy, buthave a low throughput since preparations are done one at a time. To move towardssystematic biological or medical analysis, micro- and nano-systems (MNEMS) are theappropriate tools as they can integrate accurate molecular level engineering tools andcan be cheaply produced with highly parallel process.Design and fabrication of the silicon tweezers are made by ourselves in the lab of Pr.Hiroyuki Fujita (U. of Tokyo, Japan). DNA molecules are firstly trapped in solution bydielectrophoresis. Then biological reactions are characterized in real-time by monitoringthe mechanical resonance of the system {tweezers + DNA bundle}. The resolution of themeasurements allowed the sensing of about 30 of λ-DNA molecule stiffness (i.e. about20 mN/m). To achieve the single molecule resolution, we propose to implement a feedbackstrategy to alter the system.State feedback was developed to emulate a new system more sensitive to mechanicalstiffness parameter detection. As it remains problematic to design and fabricate newmicro mechanical device with extremely low stiffness (< 1 N/m), we propose to emulate acompliant system. By simulations it was demonstrated an enhancement of the sensitivityof about 10 when the resonant frequency of the closed-loop system is designed to be 10times lower than the tweezers resonant frequency (i.e. reducing the stiffness parameterof the system). Experimentally we demonstrated an improvement of the the sensitivityof superior to 2. However the issue is here to obtain stability, robustness with respectto disturbances and unmodeled dynamics. Before to attain the sensitivity of the singlemolecule, problematics about the model of the device or about the several dynamics ofthe device needs to be dealt in order to control and fit the improvement with the theory.