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This paper addresses an H2 optimal control problem for a class of discrete-time stochastic systems with Markov jump parameter and multiplicative noises. The involved Markov jump parameter is a uniform ergodic Markov chain taking values in a Borel-measurable set. In the presence of exogenous white noise disturbance, Gramian characterization is derived for the H2 norm, which quantifies the stationary variance of output response for the considered systems. Moreover, under the condition that full information of the system state is accessible to measurement, an H2 dynamic optimal control problem is shown to be solved by a zero-order stabilizing feedback controller, which can be represented in terms of the stabilizing solution to a set of coupled stochastic algebraic Riccati equations. Finally, an iterative algorithm is provided to get the approximate solution of the obtained Riccati equations, and a numerical example illustrates the effectiveness of the proposed algorithm.

Tiltwing aircraft are a class of dual-flight-mode aircraft, which have been investigated and operated since the middle of the 20th century and combine the advantages of vertical (helicopter-mode) and horizontal (fixed-wing-mode) flight. Recent decades have witnessed a trend toward unmanned robotic aircraft (UAVs), including tiltwing designs, which has accelerated during the early 21st century. This thesis attempts to make a contribution to the understanding of the flight dynamics and control of dual-flight-mode UAVs, by presenting a mathematical model and simulation of a commercially available 1:41 scale model of the Canadair CL-84 tiltwing aircraft. Four exemplars of the full-size CL-84 were built between 1963 and 1974, and the airplane demonstrated relatively good flight characteristics, according to test-pilot accounts. The flight-dynamics model of the scale version accounts for the most relevant thrust-related and aerodynamic forces and moments. The model is simulated in the MATLAB/Simulink development environment, using a modular programming approach. Linear reduced state-space models were derived from the nonlinear dynamics model, by means of Jacobian linearization at trim points, for both helicopter-mode and fixed-wing-mode flight. Based on the state-space models, stabilizing linear tracking controllers were developed, using servomechanism linear quadratic regulator (LQR) control design. The stabilizing controllers shift the system poles to the left half-plane, balance stability and maneuverability, and are capable of counteracting input and state disturbances. The helicopter-mode and fixed-wing-mode controllers were combined during wing tilt, using a weighted sum of either controller, to develop a controller for the transition from hover to conventional forward flight and vice versa. Transition flight displays vehicle wallowing, typical of tiltwing aircraft during conversion. The modular flight-dynamics and control model is extensible, and its applicability and fidelity could be enhanced by including additional forces and moments, as well as aerodynamic derivatives, implementing gain scheduling of linear controllers extracted at multiple trim points, as well as by employing a more comprehensive controller model for stabilizing and transition control.

We consider network structures that optimize the H2 norm of weighted, time scaled consensus networks, under a minimal representation of such consensus networks described by the edge Laplacian. We show that a greedy algorithm can be used to find the minimum-H2 norm spanning tree, as well as how to choose edges to optimize the H2 norm when edges are added back to a spanning tree. In the case of edge consensus with a measurement model considering all edges in the graph, we show that adding edges between slow nodes in the graph provides the smallest increase in the H2 norm., IFAC-PapersOnLine, 54 (9), ISSN:2405-8963, 24th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2020)

20th World Congress of the International-Federation-of-Automatic-Control (IFAC) -- JUL 09-14, 2017 -- Toulouse, FRANCE, WOS: 000423964800104, In this work, the mathemtical model of a railway passenger car with conventional and radial-elastic wheels is analyzed. Stochastic excitations are applied to the wheelsets. The local elasticity between the wheel and the rail is modelled by a linearized stiffness behaviour due to geometrical effects to simplify the controller design procedure for H-2 analysis. An optimization of the vertical dynamics is performed by reducing the the H-2 norms of the dynamic wheel forces while keeping the RMS gain of carbody accelerations at a constant level. It is seen that the controller performs well on the low frequency range where the ride comfort is more pronounced and partially on the high frequency range to suppress the environmental ground vibrations and structure-borne noise, Int Federat Automat Control, Continental Automot, Occitanie Reg, Toulouse Metropole, CNES, Univ Toulouse III, Paul Sabatier, Inria, CNRS, OPTITRACK, MDPI, ISAE Supaero, iCODE, EECI, Int Journal Automat & Comp, IEEE CAA Journal Automatica Sinica, Moveo

For model based control designs like $\boldsymbol{H}_{2}$ and $\boldsymbol{H}_{\boldsymbol{\infty}}$ optimal control, the controller order is typically equal to the model order. However, the synthesis and real-time implementation of these controllers may be hampered for models of large order due to computational limitations. Several closed-loop relevant order reduction techniques have been developed in order to overcome this problem. One technique is Linear Quadratic Gaussian (LQG) balanced truncation, which is closely related to LQG and $\boldsymbol{H}_{2}$ optimal controller design. This paper demonstrates the non-optimality of this technique for constrained order $\boldsymbol{H}_{2}$ optimal controller design. Furthermore, improvements to reduce the loss of performance as a result of truncation are proposed. These improvements can be applied to a large class of controller designs and order reduction techniques as well.

In this paper, an islanded microgrid is modelled as a linear multivariable dynamic system. Then, the multivariable analysis tools are employed. The generalized Nyquist diagram and the relative gain array are used respectively for the stability assessment and solving the paring problem among the inputs and outputs. Droop control dependency on the X/R ratio of the microgrid DERs is recognized and its type is proposed using the relative gain array concept. Robust stability, nominal performance and robust performance requirements are evaluated in order to a better understanding of the system dynamics. Finally, three different controllers including H ∞ , H 2 and sequential proportional-integral-derivative controls are designed and compared.

Magneto-rheological (MR) dampers are effective solutions in improving vehicle stability and passenger comfort. However, handling these dampers implies a strong effort in modeling and control. This research proposes an H2 controller, based on a Takagi-Sugeno (T-S) fuzzy model, for a two-degrees-of-freedom (2-DOF) one-quarter vehicle semi-active suspension with an MR damper; a system with important applications in automotive industry. Regarding performance criteria (in frequency domain) handled herein, the developed controller considerably improves the passive suspension's efficiency. Moreover, nonlinear actuator dynamics usually avoided in reported work, is included in controller's synthesis; improving the relevance of research outcomes because the controller is synthesized from a closer-to-reality suspension model. Going further, outcomes of this research are compared (based on frequency domain performance criteria and a common time domain test) with reported work to highlight the outstanding results. H2 controller is given in terms of quadratic Lyapunov stability theory and carried out by means of Linear Matrix Inequalities (LMI), and the command signal is applied via the Parallel Distributed Compensation (PDC) approach. A case of study, with real data, is developed and simulation work supports the results. The methodology applied herein can be extended to include other vehicle suspension's dynamics towards a general chassis control. © 2016 Universidad Nacional Autónoma de México, Centro de Ciencias Aplicadas y Desarrollo Tecnológico.

This paper presents an algebraic approach to polynomial spectral factorization, an important mathematical tool in signal processing and control. The approach exploits an intriguing relationship between the theory of Gröbner bases and polynomial spectral factorization which can be observed through the sum of roots, and allows us to perform polynomial spectral factorization in the presence of real parameters. It is discussed that parametric polynomial spectral factorization enables us to express quantities such as the optimal cost in terms of parameters and the sum of roots. Furthermore an optimization method over parameters is suggested that makes use of the results from parametric polynomial spectral factorization and also employs two quantifier elimination techniques. This proposed approach is demonstrated in a numerical example of a particular control problem.

Este trabalho tem como objetivo o estudo de estabilidade de sistemas lineares com comutação sujeitos à perturbações impulsivas tendo em vista o projeto de controle via realimentação de estado com comutação. As condições obtidas são baseadas nas desigualdades de Lyapunov-Metzler, que asseguram a estabilidade mesmo quando o sistema evoluir sobre um modo deslizante. Estas desigualdades permitem levar em conta um custo garantido de desempenho. De forma a analisar a qualidade do resultado, um limitante inferior para o custo verdadeiro é determinado. A teoria desenvolvida é aplicada em um problema de controle H2 multiobjetivo com critérios possivelmente conflitantes. É mostrado que, neste contexto, o uso de controle com comutação fornece resultados melhores quando comparados com outros métodos encontrados na literatura. Exemplos acadêmicos são usados para ilustração. This work aims at studying the stability of switched linear systems with impulsive disturbances and at designing a state feedback switched control. The conditions are based on Lyapunov-Metzler inequalities, which assure that stability is preserved even if the system evolves on a sliding mode. A slight modification of these inequalities is introduced to cope with a guaranteed cost performance. In order to analyze the quality of the proposed solution, a lower bound for the actual cost is calculated. The theoretical results are applied to a multiobjective H2 control design problem with a number of possibly conflicting criteria. It is shown that the use of switched linear systems theory in multiobjective H2 control problems provides better results than others methods available in the literature. Academic examples are used for illustration.

In this paper the H2-optimal control problem of systems with multiple i/o delays is presented. The problem is first converted to an equivalent H2 regulator problem with multiple delays. The idea is to view the regulator problem in time-domain as a linear quadratic regulator problem with multiple input delays. It is shown that the rational part of the optimal controller has the same dimension as the plant and the non-rational part may be chosen to have finite impulse response. Furthermore, the regulator problem solution is also used to solve the H2 filtering problem with multiple measurement delays.

Narrow tilting vehicles (NTVs) are the convergence of a car and a motorcycle. They are expected to be the new generation of city cars considering their practical dimensions and lower energy consumption. However, due to their height-to-breadth ratio, in order to maintain lateral stability, NTVs should tilt when cornering. Unlike the motorcycle, where the driver tilts the vehicle himself, the tilting of an NTV should be automatic. Two tilting systems are available, i.e., direct tilt control (DTC) and steering tilt control (STC), the combined action of these two systems being certainly the key to considerably improve NTV dynamic performances. In this paper, multivariable control tools ( $H_{2}$ methodology) are used to design, in a systematic way, lateral assistance controllers driving DTC, STC, or both DTC/STC systems. A three-degree-of-freedom (DoF) model of the vehicle is used, as well as a model of the steering signal, leading to a two-DoF low-order controller with an efficient feedforward anticipative part. Taking advantage of all the available measurements on NTVs, the lateral acceleration is directly regulated. Finally, a gain-scheduling solution is provided to make the DTC, STC, and DTC/STC controllers robust to longitudinal speed variations.

In advanced process control, the Model Predictive Control (MPC) may be considered the most important innovation in recent years and the standard tool for industrial applications due to the fact that it keeps the plant operating in the constraints more profitable. However, like every control algorithm, the MPC after some time in operation rarely works as originally designed. Thus, to preserve the benefits of MPC systems for a long period of time, their performance needs to be monitored and evaluated during the operation. This task require the presence of reliable and effective tools to detect when the controller performance is below of the desirable, to define the need, or not, of recommissioning the system. Thus, the objective of this work is development of techniques for monitoring and evaluating the performance of multivariable predictive controllers, being developed two new tools: LQG benchmark Modified and IHMC benchmark. The results obtained from numerical simulations were satisfactory and consistent with the technical literature applied in the developments of the evaluators, which were used in the monitoring of the control system MPC of the oil-water-gas three-phase separation process, offering an appropriate solution and providing subsidies for implementations in real industrial systems. Em controle avançado de processos, o controlador preditivo ou MPC (Model Predictive Control) pode ser considerado como a mais importante inovação dos últimos anos e a ferramenta padrão para aplicações industriais, devido ao fato do MPC manter a planta operando dentro das suas restrições de forma mais lucrativa. Entretanto, como todo algoritmo de controle, o MPC depois de algum tempo em operação dificilmente funciona como quando fora inicialmente projetado. Desta forma, com o objetivo de manter os benefícios dos sistemas MPC por um longo período de tempo, seu desempenho precisa ser monitorado e avaliado durante a operação. Esta tarefa requer a presença de ferramentas efetivas e confiáveis para detectar quando o desempenho do controlador estiver abaixo do desejável, para definir a necessidade, ou não, de um recomissionamento do sistema. Destarte, aborda-se neste trabalho o desenvolvimento de técnicas para monitoramento e avaliação de desempenho de controladores preditivos multivariáveis, sendo desenvolvidas duas novas ferramentas: LQG benchmark Modificado e IHMC benchmark. Os resultados obtidos a partir de simulações numéricas foram satisfatórios e coerentes com a literatura técnica aplicada no desenvolvimento dos avaliadores, os quais foram utilizados no monitoramento do sistema de controle MPC do processo de separação trifásica água-óleo-gás, oferecendo assim uma solução apropriada e fornecendo subsídios para implementações em sistemas industrias reais.

International audience; In control design, a particular method consists in two main steps. Firstly, a global model is defined by embodying both, the system to be controlled and an exosystem (regrouping reference and disturbances models). Secondly, a standard H2 (or H1) optimization problem is defined. Formerly named the Disturbance Modeling method in the LQG context, the control goal is to minimize a quadratic index by weighting the output reference error in one side, and the control input in the other. In the case where the exosystem is unstable because e.g. persistent disturbances, this index is not bounded. It is then possible to change the criterion, weighting the ad hoc control input and output deviation to make the problem well posed (comprehensively stabilizable). The current paper deals with the same framework for stable exosystems and unstable ones, and proposes a systematic way to get a well-posed control optimization problem leading to a 2 Degree of Freedom controller.

Narrow Tilting Vehicles (NTV) are the convergence of a car and a motorcycle. One meter wide, these vehicles are designed for one or two people sitting the one in front the other. The idea behind the conception of NTV is the minimization of traffic congestion, energy consumption and pollutant emission. But because of their dimensions, these cars would have to lean into corners in order to compensate for the lateral acceleration and maintain their stability. The tilting should be automatic, and can be achieved by a tilting torque generated by a dedicated tilting actuator (DTC) or by modifying the steering angle (STC) or both (SDTC). In this thesis, we first propose a methodology for the design of an output feedback structured regulator, minimizing the H2 norm of a well-posed problem, built to optimize the lateral acceleration of the NTV, considering DTC and SDTC systems.The designed controllers, with the longitudinal velocity as a parameter, lead to the minimization of the tilting torque and of the lateral acceleration perceived by the driver, and have good performances as well as good robustness properties. Furthermore, the tuning methodology allows the comparison of a pure DTC solution and a mixed SDTC alternative. Compared to the literature, the originalities in this thesis are the direct control of the measured value of the lateral acceleration (instead of the tilting angle), and the anticipation of the tilt, thanks to the use of the steering angle and angular velocity. Furthermore, the SDTC solution allows to drive both the STC and DTC systems in a coordinated manner. The design strategies are based on a preliminary study of vehicle models, and a design model with 5DoF was developed. We demonstrated that the model has the nice property to be flat, and in the last section of the thesis, used this property to initiate the design of a non-linear robust controller, which can a priori lead to better performances in case of “large motions”.; Les Véhicules Etroits et Inclinables (VEI) sont la convergence d’une voiture et d’un motocycle. Un mètre de largeur seulement suffit pour transporter une ou deux personnes en Tandem. Les VEI sont conçus dans le but de résoudre partiellement les problèmes de trafic routier, de minimiser la consommation énergétique et l’émission de polluants. De par leurs dimensions(ratio hauteur/largeur), ces véhicules doivent s’incliner en virage pour rester stable en compensant l’effet de l’accélération latérale. Cette inclinaison doit dans certains cas être automatique : elle peut être réalisée à l’aide d’un couple d’inclinaison généré par un actionneur dédié (système DTC), soit encore en modulant l’angle de braquage des roues (Système STC). Nous avons proposé dans ce mémoire une méthodologie de synthèse d’un régulateur structuré minimisant la norme H2 d’un problème bien posé au bénéfice d’une régulation optimisée de l’accélération latérale, considérant tour à tour les systèmes DTC et STC. Les régulateurs proposés sont paramétrés par la vitesse longitudinale et s’avèrent performants et robustes, et les moyens de réglages proposés permettent d’étudier l’intérêt relatif d’une solution DTC pure ou mixte DTC/STC, permettant de supporter les développements futurs sur le sujet. L’originalité des solutions proposées en regard des études rencontrées dans la littérature porte en particulier sur le fait de choisir de réguler directement l’accélération latérale perçue (plutôt que l’angle d’inclinaison), en anticipant la prise de virage par la prise en compte des angles et vitesse de braquage. L’optimisation de la régulation permet de réduire de manière importante le couple d’inclinaison requis, et l’accélération latérale subie par les passagers est faible. Tous les développements proposés s’appuient naturellement en amont sur un travail de modélisation (recherche du modèle juste nécessaire), et de bibliographie conséquent. Le modèle retenu comprend 5 degrés de libertés. Nous avons démontré qu’il possédait la propriété intéressante d’être plat, et avons utilisé cette propriété pour ouvrir des perspectives relatives à la conception d’un régulateur non-linéaire robuste, susceptible apriori d’accroître les performances dans le cas de « grands mouvements ». Au contraire de ce qui existe dans la littérature,le régulateur multivariable conçu pour le système SDTC permet le contrôle coordonné des actions sur les systèmes STC et DTC.

We present in this paper an analysis of several tip-tilt on-sky data registered on adaptive optics systems installed on different telescopes (Gemini South, William Herschel Telescope, Large Binocular Telescope, Very Large Telescope, Subaru). Vibration peaks can be detected, and it is shown that their presence and location may vary, and that their origin is not always easy to determine. Mechanical solution that have been realized to mitigate vibrations are presented. Nevertheless, residual vibrations may still affect the instruments' performance, ranging from narrow high frequency vibration peaks to wide low frequency windshake-type perturbations. Power Spectral Densities (PSDs) of on-sky data are presented to evidence these features. When possible, indications are given regarding the gain in performance that could be achieved with adequate controllers accounting for vibration mitigation. Two examples of controller identification and design illustrate their ability to compensate for various types of disturbances (turbulence, windshake, vibration peaks, ...), showing a significant gain in performance. © 2012 SPIE., Adaptive Optics Systems III, July 1-6, 2012, Amsterdam, the Netherlands, Series: Proceedings of SPIE; no. 8447

International audience; HIFOO is a public-domain Matlab package initially designed for Hinfinity fixed-order controller synthesis, using nonsmooth nonconvex optimization techniques. It was later on extended to multi-objective synthesis, including strong and simultaneous stabilization under Hinfinity constraints. In this paper we describe a further extension of HIFOO to H2 performance criteria, making it possible to address mixed H2/Hinfinity synthesis. We give implementation details and report our extensive benchmark results.

International audience; HIFOO is a public-domain Matlab package initially designed for Hinfinity fixed-order controller synthesis, using nonsmooth nonconvex optimization techniques. It was later on extended to multi-objective synthesis, including strong and simultaneous stabilization under Hinfinity constraints. In this paper we describe a further extension of HIFOO to H2 performance criteria, making it possible to address mixed H2/Hinfinity synthesis. We give implementation details and report our extensive benchmark results.

International audience; HIFOO is a public-domain Matlab package initially designed for Hinfinity fixed-order controller synthesis, using nonsmooth nonconvex optimization techniques. It was later on extended to multi-objective synthesis, including strong and simultaneous stabilization under Hinfinity constraints. In this paper we describe a further extension of HIFOO to H2 performance criteria, making it possible to address mixed H2/Hinfinity synthesis. We give implementation details and report our extensive benchmark results.

Este artigo fornece condições convexas com convergência garantida para o projeto de controladores por realimentação de estados que estabilizam quadraticamente e também asseguram desempenhos ótimos H2 e H∞ sob estabilidade quadrática para sistemas nebulosos de Takagi-Sugeno contínuos no tempo. As condições propostas são formuladas como desigualdades matriciais lineares (LMIs) dependentes de parâmetros com variáveis de folga provenientes do Lema de Finsler e com parâmetros pertencentes ao simplex unitário. A lei de controle nebulosa é dada por um ganho de realimentação de estados que é um polinômio homogêneo de grau g, que tem como caso particular o compensador paralelo distribuído quando g = 1. Propriedades algébricas dos parâmetros do sistema e resultados recentes sobre positividade de polinômios são usados para construir relaxações LMIs que, diferentemente da maioria das relaxações da literatura, convergem assintoticamente para a solução sempre que esta existir. Graças ao grau de liberdade obtido pelo uso de variáveis de folga, as condições apresentadas no artigo representam avanços em relação a condições recentemente publicadas baseadas no Teorema de Pólya, e podem ser vistas como uma alternativa a técnicas baseadas na relaxação de formas quadráticas. A eficiência numérica em termos de precisão e esforço computacional é demonstrada por meio de comparações com outros métodos da literatura. This paper provides convex conditions with certificates of convergence for the design of state feedback controllers that quadratically stabilize and also ensure optimal H2 and H∞ performances under quadratic stability for Takagi-Sugeno continuous-time fuzzy systems. The proposed conditions are formulated as parameter-dependent linear matrix inequalities (LMIs) that have extra variables from Finsler's lemma and parameters belonging to the unit simplex. The fuzzy control law is written as a state feedback gain that is a homogeneous polynomial of degree g, encompassing the parallel distributed compensator as a special case when g = 1. Algebraic properties of the system parameters and recent results of positive polynomials are used to construct LMI relaxations which, differently from most relaxations in the literature, asymptotically converge to a solution whenever such solution exists. Due to the degree of freedom obtained with the extra variables, the conditions presented in the paper are an improvement over earlier results based on Pólya's theorem and can be viewed as an alternative to the use of techniques based on the relaxation of quadratic forms. The numerical efficiency in terms of precision and computational effort is demonstrated by means of comparisons with other methods from the literature.

National audience; This article deals with the problematic of micro- and nanoforce measurement. The force is the unknown excitatory signal of a transducer whose only the output is measurable. This general problematic of an unknown input signal reconstruction from a noisy output signal is developed inside the H2 synthesis framework. The resulting methodology is implemented in a micro- and nanoforce sensor that uses a macroscopic seismic mass controlled by active magnetic springs. This methodology uses only a very basic knowledge on the force dynamic and thanks to H2 synthesis, ensures that the force estimation remains correct despite the transducer dynamic, the noise measurement, the uncertainty on the force dynamic and the sensor modeling errors.

International audience; In web transport systems, the main problem is to control the web velocity and tensions independently, to prevent web breaks, folding, or damage. Interesting results have been obtained using multi-variable control strategies. Unfortunately, most of the existing methodologies are either not systematic or deal with the tracking and disturbance rejection problems as a whole, and not separately. This paper presents a complete methodology in order to design two-degrees-of-freedom (2DOF) controller. The feedforward part is based on a reference model allowing operators to obtain the desired tracking performances (in particular, web tensions and velocity decoupling). The feedback part ensures robustness and disturbance rejection and is designed using two high-level tuning parameters only, thanks to the Standard State Control (SSC) methodology. However, the system dynamics change greatly during the winding/unwinding process due to the winder/unwinder radius and inertia variations. Therefore, a gain-scheduling controller is derived from the interpolation of consistent realizations of the H2 controllers obtained at different points of the operating domain. The resulting controller is tested on a realistic simulator first, and after discretization, on a 3-motor web-handling experimental platform

In web transport systems, the main problem is to control the web velocity and tensions independently, to prevent web breaks, folding, or damage. Interesting results have been obtained using multi-variable control strategies. Unfortunately, most of the existing methodologies are either not systematic or deal with the tracking and disturbance rejection problems as a whole, and not separately. This paper presents a complete methodology in order to design two-degrees-of-freedom (2DOF) controller. The feedforward part is based on a reference model allowing operators to obtain the desired tracking performances (in particular, web tensions and velocity decoupling). The feedback part ensures robustness and disturbance rejection and is designed using two high-level tuning parameters only, thanks to the Standard State Control (SSC) methodology. However, the system dynamics change greatly during the winding/unwinding process due to the winder/unwinder radius and inertia variations. Therefore, a gain-scheduling controller is derived from the interpolation of consistent realizations of the H2 controllers obtained at different points of the operating domain. The resulting controller is tested on a realistic simulator first, and after discretization, on a 3-motor web-handling experimental platform.

International audience; no abstract

International audience; no abstract

This paper investigates the design of an “extended” state-feedback H 2 controller for continuous-time descriptor systems. In such problem, the controller, which is in descriptor form, is found such that : - The closed-loop transfer matrix is strictly proper and has minimum H 2 -norm. - Only the internal stability of the physical system (and not the overall descriptor standard model) is required. An explicit characterization of the solution based on a generalized algebraic Riccati equation and two Sylvester equations is given. Under some additional assumptions, a LMI-based solution is proposed. A numerical example is also included to show the applicability of the proposed results.

International audience; In this paper we compare LTI and qLPV Hinfinity/H2 controllers. The Pareto limit is used to show the compromise that has to be done when a mixed synthesis is achieved. Simulations on a nonlinear half vehicle model, with multiple objectives, are performed to show the efficiency of the method.

Nowadays, the control designer has to deal with more and more complex systems, with a high number of dynamics, but also of actuators and captors, or even spatial structural constraints on the controller. This comes from the increasing complexity of industrial processes, the use of more and more efficient communication systems, and increasing performances requirements (optimization as global as possible).Even if decentralized control theory has benefit from numerous studies since the 70's, many problems are still opened. At the same time, efficient tools for analysis and synthesis have been developed, especially in the H2 and the H¥ context. However, application of such tools in the case of large-scale systems (composed most of the time of interconnected subsystems) may be difficult, even more if structural constraints are applied to the controller.Methodology is essential when the control problem of complex system is considered. To this end, this document focuses on the analysis of the interconnections of subsystems in order to choose the most appropriated structure for the controller. The choice of the criterion, and the global optimization of a H2 controller in a sequential manner are also considered. These methodological considerations are applied on an experimental web transport system.; Davantage que par le passé, le concepteur de lois de commande se trouve confronté à des systèmes complexes : nombre élevé de dynamiques mais aussi d'actionneurs et de capteurs, voire contraintes spatiales sur la structure du régulateur. Ceci résulte de la complexification croissante des processus industriels, de l'avènement de systèmes de communication performants ainsi que de la recherche de performances accrues (recherche d'une optimisation plus globale).Si la commande décentralisée a mobilisé de nombreux efforts de recherche dés les années 70, de nombreux problèmes restent ouverts. Dans le même temps, des outils d'analyse et de synthèse performants ont été développés, dans le cadre H2 et H¥ notamment. Leur mise en œuvre pour de très grands systèmes (composés le plus souvent de sous-systèmes interconnectés) peut cependant poser problème, et ce d'autant que des contraintes de structure sont appliquées au correcteur.L'élaboration de commandes pour les systèmes complexes requiert à l'évidence de la méthodologie. A cette fin, ce document s'intéresse à l'analyse des interconnexions internes au système pour choisir la structure du régulateur la mieux appropriée. Il considère également la problématique du choix du critère et la possibilité d'aborder séquentiellement l'optimisation globale d'un correcteur H2. Ces réflexions à caractère méthodologique sont mises en œuvre sur un système expérimental (multi-moteurs) d'entraînement de bande flexible.

In this paper the H2-optimal control problem of systems with multiple i/o delays is presented. The problem is first converted to an equivalent H2 regulator problem with multiple delays. The idea is to view the regulator problem in time-domain as a linear quadratic regulator problem with multiple input delays. It is shown that the rational part of the optimal controller has the same dimension as the plant and the non-rational part may be chosen to have finite impulse response. Furthermore, the regulator problem solution is also used to solve the H2 filtering problem with multiple measurement delays.

International audience; no abstract

A new approach for LQ optimal control of SISO discrete linear systems is presented. We solve a constrained Wiener-Hopf problem, stated in the time domain, where the constraints originate from the structure at infinity of the plant transfer function. These are consequences due to the requirement for properness of the compensator transfer function. Plants are assumed to be minimum-phase.

This paper is addressed to the vibration control of an elastic plate, clamped along one side and excited by an impulsive transversal force acting in correspondence of a free corner. The plate is equipped with three couples of piezoelectric patches, used as sensors and actuators. A modal model of the coupled electromechanical structure, obtained by employing a suitable finite-element formulation together with a modal reduction, is used in the controller design. Different H2 control laws have been designed and compared by simulation, in order to evaluate the performance obtained using different combinations of sensors and actuators together with models taking into account an increasing number of structural eigenmodes.

Filtering of linear dynamical systems has historically been accomplished through the application of the Kalman filter. The Kalman filter has a minimum mean squared error type performance for linear systems with stochastic inputs. In practice, the Kalman filter has been adapter for use with systems outside its usual solution set. For example, the extended Kalman filter for nonlinear systems. While the Kalman filter has been rather successful in general, practical applications have found that model uncertainty and non-stochastic inputs are problematic. To resolve same of these issues, filters based on alternative performance criteria have been developed. One of these is the H2 filter which has a minimum error energy type performance for linear systems with unknown deterministic inputs. Another is the H- filter, which places a bound on the energy gain from the deterministic inputs to the filter error.Application of the H2 filter follows the same type of methodology as the Kalman filter. In fact, the structure of the filter and the filter algorithms are quite similar. Application of the H- filter has been sporadic because its methodology is more complicated and more poorly understood. In fact, the structure of the H- filter and filter algorithms also has some similarity with the structure of the Kalman filter.In this thesis, the similarities between the structure of the H-, H2, and Kalman filters are examined. The filters used in this examination have been derived through duality to the full information controller. In addition, a direct variation of parameters derivation of the H- filter is presented for both continuous and discrete time (scaler case). Direct and controller dual derivations using differential games exist in the literature and also employ variational techniques. Using a variational, rather than a differential games, viewpoint has resulted in a simple relationship between the Riccati equations that arise from the derivation and the results of the Bounded Real Lemma. This same relation has previously been found in the literature and used to relate the Riccati inequality for linear systems to the Hamilton Jacobi inequality for nonlinear systems when implementing the H- controller.The H-, H2, and Kalman filters are applied to the two-state target tracking problem. In continuous time, closed form analytic expressions for the trackers and their performance are determined. To evaluate the trackers using a neutral, realistic, criterion, the probability of target escape was developed. That is, the probability that the target position error will be such that the target is outside the radar beam width resulting in a loss of measurement. In discrete time, a numerical example, using the probability of target escape, is presented to illustrate the differences in performance of the trackers.

This paper presents necessary and sufficient conditions for the existence of a quadratically stabilizing output feedback controller which also assuresH2guaranteed cost performance on a discrete linear uncertain system where the uncertainty is of the norm bounded type. The conditions are presented as a collection of linear matrix inequalities.The solution, however requires a search over a scalar parameter space.

The open loop F-18 longitudinal control system is stabilized using H2 and H-infinity singular value loop shaping for a multivariable feedback control system. The H2 and H-infinity control theories involve suppressing the sensitivity matrix transfer function at the lower frequencies for high gain performance and suppressing the transmissivity at higher frequencies, i.e., loop shaping. The singular value Bode plot is used for MIMO systems in analogy with the classical Bode frequency analysis for SISO (Single Input Single Output) systems. There are two control inputs with input 1 controlling the stabilator and input 2 controlling the leading edge flap and trailing edge flap in tandem. There are two output: angle of attack and pitch rate. The H-infinity design achieved a separation in that input 1 controlled angle of attack and input 2 controlled pitch rate. the first design is an optimum design which imposed no limitations on control input. A cost penalty associated with control actuator limitations is imposed to achieve a limited performance design. http://archive.org/details/frobustcontrolde1094534898 Aerospace Engineer, Naval Weapons Center author (civilian). Approved for public release; distribution is unlimited.

This paper deals with the robust H2 fuzzy observer-based control problem for discrete-time uncertain nonlinear systems. The Takagi and Sugeno (T–S) fuzzy model is employed to represent a discrete-time nonlinear system with parametric uncertainties. A fuzzy observer is used to estimate the state of the fuzzy system and a non-parallel distributed compensation (non-PDC) scheme is adopted for the control design. A fuzzy Lyapunov function (FLF) is constructed to derive a sufficient condition such that the closed-loop fuzzy system is globally asymptotically stable and an upper bound on the quadratic cost function is provided. A sufficient condition for the existence of a robust H2 fuzzy observer-based controller is presented in terms of linear matrix inequalities (LMIs). Moreover, by using the existing LMI optimization techniques, a suboptimal fuzzy observer-based controller in the sense of minimizing the cost bound is proposed. Finally, an example is given to illustrate the effectiveness of the proposed design method.

In this paper, we use the Youla parameterization for an uncertain LTI system to characterize the set of all stabilizing controllers. Next, this set is used as a search space to find the controller which minimizes ?2 norm of the transfer function from disturbance to output. Finally, this methodology is used for stabilization of a 8-th order plant affected by parametric uncertainty describing a voice coil motor (VCM) of a hard disk drive (HDD).

The objective of this dissertation is to develop data-driven frequency-domain methods for designing robust controllers through the use of convex optimization algorithms. Many of today's industrial processes are becoming more complex, and modeling accurate physical models for these plants using first principles may be impossible. Albeit a model may be available; however, such a model may be too complex to consider for an appropriate controller design. With the increased developments in the computing world, large amounts of measured data can be easily collected and stored for processing purposes. Data can also be collected and used in an on-line fashion. Thus it would be very sensible to make full use of this data for controller design, performance evaluation, and stability analysis. The design methods imposed in this work ensure that the dynamics of a system are captured in an experiment and avoids the problem of unmodeled dynamics associated with parametric models. The devised methods consider robust designs for both linear-time-invariant (LTI) single-input-single-output (SISO) systems and certain classes of nonlinear systems. In this dissertation, a data-driven approach using the frequency response function of a system is proposed for designing robust controllers with $\mathcal{H}_{\infty}$ performance. Necessary and sufficient conditions are derived for obtaining $\mathcal{H}_{\infty}$ performance while guaranteeing the closed-loop stability of a system. A convex optimization algorithm is formulated to obtain the controller parameters which ensure system robustness; the controller is robust with respect to the frequency-dependent uncertainties of the frequency response function. For a certain class of nonlinearities, the proposed method can be used to obtain a best-linear-approximation with an associated frequency-dependent uncertainty to guarantee the stability and performance for the underlying linear system that is subject to nonlinear distortions. The controller for this design scheme is presented as a ratio of two linearly-parameterized transfer functions; in this manner, the numerator and denominator of a controller are simultaneously optimized. With this construction, it can be shown that as the controller order increases, the solution to the convex problem converges to the global optimal solution of the $\mathcal{H}_{\infty}$ problem. This method is then extended to the 2-degree-of-freedom discrete-time controller where the necessary and sufficient conditions are imposed for multiple weighted sensitivity functions. The concepts behind these design methods are then used to devise necessary and sufficient conditions for ensuring the closed-loop stability of systems with sector-bounded nonlinearities. The conditions are simple convex feasibility constraints which can be used to stabilize systems with multi-model uncertainty. Additionally, a method is proposed for obtaining $\mathcal{H}_{\infty}$ performance for systems with uncertain gains within these sectors. By convexifying the $\mathcal{H}_{\infty}$ problem, the global optimal solution to an approximate problem is obtained. For low-order controllers, the solution to this approximate problem may lead to solutions far from the optimal solution of the true $\mathcal{H}_{\infty}$ problem. Thus two methods are proposed to address this issue for low-order controllers. In one method, a non-convex problem is formulated which optimizes the basis function parameters of a controller while guaranteeing the stability of the closed-loop systems. In another method, a set of convex problems are solved in an iterative fashion to obtain the desired performance (which also guarantees the closed-loop stability of the system). With both methods, the local solution to the $\mathcal{H}_{\infty}$ problem for fixed-structure controllers is obtained. However, the convex problem is computationally tractable and can also consider $\mathcal{H}_2$ performance. The effectiveness of the proposed method(s) is illustrated by considering several case studies that require robust controllers for achieving the desired performance. The main applicative work in this dissertation is with respect to a power converter control system at the European Organization for Nuclear Research (CERN) (which is used to control the current in a magnet to produce the desired field in controlling particle trajectories in particle accelerators). The proposed design methods are implemented in order to satisfy the challenging performance specifications set by the application while guaranteeing the system stability and robustness using data-driven design strategies.