H

This paper investigates the problem of H∞ filtering for class discrete-time Lipschitz nonlinear singular systems with measurement quantization. Assume that the system measurement output is quantized by a static, memoryless, and logarithmic quantizer before it is transmitted to the filter, while the quantizer errors can be treated as sector-bound uncertainties. The attention of this paper is focused on the design of a nonlinear quantized H∞ filter to mitigate quantization effects and ensure that the filtering error system is admissible (asymptotically stable, regular, and causal), while having a unique solution with a prescribed H∞ noise attenuation level. By introducing some slack variables and using the Lyapunov stability theory, some sufficient conditions for the existence of the nonlinear quantized H∞ filter are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is presented to demonstrate the effectiveness of the proposed quantized filter design method

Analysis, filtering, and control for Takagi-Sugeno fuzzy models in networked systems

Copyright © 2015 Sunjie Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The fuzzy logic theory has been proven to be effective in dealing with various nonlinear systems and has a great success in industry applications. Among different kinds of models for fuzzy systems, the so-called Takagi-Sugeno (T-S) fuzzy model has been quite popular due to its convenient and simple dynamic structure as well as its capability of approximating any smooth nonlinear function to any specified accuracy within any compact set. In terms of such a model, the performance analysis and the design of controllers and filters play important roles in the research of fuzzy systems. In this paper, we aim to survey some recent advances on the T-S fuzzy control and filtering problems with various network-induced phenomena. The network-induced phenomena under consideration mainly include communication delays, packet dropouts, signal quantization, and randomly occurring uncertainties (ROUs). With such network-induced phenomena, the developments on T-S fuzzy control and filtering issues are reviewed in detail. In addition, some latest results on this topic are highlighted. In the end, conclusions are drawn and some possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 11301118 and 61174136, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the Fundamental Research Funds for the Central Universities of China under Grant CUSF-DH-D-2013061, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey

The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H ∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Stabilization for a class of rectangular descriptor systems via time delayed dynamic compensator

Abstract: This paper focuses on the stabilization problem for a class of rectangular descriptor systems through dynamic compensation. Such class of systems may not be stabilized by delayfree dynamic compensators, while delayed dynamic compensator could achieve such purpose. We provide a design scheme of time-delayed dynamic compensator which makes the closed-loop system admissible. The design involves solving a quadratic matrix inequality, and consequently, we build a linear matrix inequality (LMI) based algorithm to compute compensator gains. We verify that, under certain circumstances for which delay-free dynamic compensators fail to stabilize, the proposed method works well. An illustrative example demonstrates the usefulness of the present scheme

Observer based active fault tolerant control of descriptor systems

The active fault tolerant control (AFTC) uses the information provided by fault detection and fault diagnosis (FDD) or fault estimation (FE) systems offering an opportunity to improve the safety, reliability and survivability for complex modern systems. However, in the majority of the literature the roles of FDD/FE and reconfigurable control are described as separate design issues often using a standard state space (i.e. non-descriptor) system model approach. These separate FDD/FE and reconfigurable control designs may not achieve desired stability and robustness performance when combined within a closed-loop system.This work describes a new approach to the integration of FE and fault compensation as a form of AFTC within the context of a descriptor system rather than standard state space system. The proposed descriptor system approach has an integrated controller and observer design strategy offering better design flexibility compared with the equivalent approach using a standard state space system. An extended state observer (ESO) is developed to achieve state and fault estimation based on a joint linear matrix inequality (LMI) approach to pole-placement and H∞ optimization to minimize the effects of bounded exogenous disturbance and modelling uncertainty. A novel proportional derivative (PD)-ESO is introduced to achieve enhanced estimation performance, making use of the additional derivative gain. The proposed approaches are evaluated using a common numerical example adapted from the recent literature and the simulation results demonstrate clearly the feasibility and power of the integrated estimation and control AFTC strategy. The proposed AFTC design strategy is extended to an LPV descriptor system framework as a way of dealing with the robustness and stability of the system with bounded parameter variations arising from the non-linear system, where a numerical example demonstrates the feasibility of the use of the PD-ESO for FE and compensation integrated within the AFTC system.A non-linear offshore wind turbine benchmark system is studied as an application of the proposed design strategy. The proposed AFTC scheme uses the existing industry standard wind turbine generator angular speed reference control system as a “baseline” control within the AFTC scheme. The simulation results demonstrate the added value of the new AFTC system in terms of good fault tolerance properties, compared with the existing baseline system

H2 and H∞ Filtering for Nonlinear Singular Systems

RÉSUMÉ Dans les dernières années, les systèmes singuliers des équations différentielles ont carrément explosé puisqu’on les trouve dans plusieurs champs d’applications allant des systèmes électromécaniques en passant par des circuits électroniques, réacteurs chimiques et/ou biologiques ainsi que les systèmes d’écoulement des fluides. Dans cette thèse, deux classes des systèmes singuliers non linéaires seront considérer, en l’occurrence : (i) systèmes singuliers perturbés, (ii) systèmes généralisés ou systèmes algébro-différentielles. Les techniques H2 et H∞ pour l’estimation de l’état de ces classes seront développés ainsi que des conditions suffisantes pour la résolution des problèmes en termes des équations d’Hamilton-Jacobi seront présentés. Deux systèmes, temps-continu et discrets, seront considérés et, pour plus de viabilité des résultats, des exemples pratiques seront présentés et résolus.----------ABSTRACT Singular systems of differential equations arise in many areas of science and technology, including electro-mechanical systems, electronic circuits, chemical and biological reactors, and fluid flow systems. In this thesis, two classes of singular nonlinear systems are considered; namely, (i) singularly perturbed systems, and (ii) generalized systems, or descriptor, or differential-algebraic systems. H2 and H∞ techniques for state estimation of these classes of systems are developed, and sufficient conditions for the solvability of the problems in terms of Hamilton-Jacobi equations are presented. Both continuous-time and discrete-time systems are considered, and examples are presented to show the usefulness of the results

Filtrage et commande basée sur un observateur pour les systèmes stochastiques

This thesis deals with the filtering and control of nonlinear systems described by Itô stochastic differential equations whose diffusion is controlled by a noise which is multiplied with the state vector. The noise is a Wiener process, also known as Brownian motion. When the noise is multiplied with the state in a differential equation, it can stabilize or destabilize the system, which is not the case when the noise occurs additively with respect to the state. In addition, there are several types of stability for the systems described by stochastic differential equations, some being more conservative than others. In this manuscript, the goal is to relax the conditions of stability used in the literature using the almost sure exponential stability, also called exponential stability with probability equal to one. Three main fields are treated in this manuscript :(i) observers synthesis, (ii) stability and stabilization of stochastic systems, (iii) bounded real lemma for stochastic algebro-differential systems.A new theorem on the almost sure exponential stability of the equilibrium point of a class of triangular nonlinear stochastic systems is proposed : the stability of the whole system is ensured by the stability of each decoupled subsystem. The proof of this result is based on the boundedness of the Lyapunov exponents. It was shown that the problem of filtering of stochastic systems with multiplicative noises by imposing the almost sure exponential stability of the observation error can not be solved by using the Lyapunov type approaches available in the literature. This difficulty was overcome by using the triangular structure, associated with this filtering problem, which allows to split the original observer design problem into two decoupled subproblems : (i) demonstrate the stability of the stochastic differential equation describing the dynamics of the state to be estimated, (ii) stabilize the stochastic differential equation describing the dynamics of the observation error. This approach is based on the new theorem on the almost sure exponential stability of a class of Lipschitz triangular nonlinear stochastic systems mentioned above. This has been extended to nonlinear stochastic systems with one-sided Lipschitz nonlinearities. To ensure the stability of the observation error, a polytopic approach was proposed with a “descriptor” formalism (or algebro-differential). The results presented above have been extended to the synthesis of robust observers in the presence of parametric uncertainties. Conditions for asymptotic rejection of perturbations occurring in a stochastic differential equation with multiplicative noises have been proposed. The considered stability is the almost sure exponential one. A bound of the Lyapunov exponent ensures the almost sure convergence rate to zero for the state of the system. A bang-bang control law is synthesized for a class of stochastic nonlinear systems in two cases : (i) state feedback and (ii) measured output feedback with an observer. The used stability is the almost sure exponential one. A version of the bounded real lemma is developed for stochastic algebro-differential systems (also called singular systems or descriptor systems) with multiplicative noises. This work required the development of Itô formula in the case of nonlinear stochastic algebro-differential equations. This approach has been used for the synthesis of an H∞ measured output feedback control law with the exponential mean square stability. An observer for nonlinear stochastic algebro-differential systems was proposed using the almost sure exponential stability.Ce mémoire de thèse traite du filtrage et de la commande des systèmes non linéaires décrits par des équations différentielles stochastiques au sens d’Itô dont la diffusion est commandée par un bruit qui intervient de manière multiplicative avec l’état. Ce bruit est un processus de Wiener, aussi appelé mouvement brownien. Lorsque le bruit agit de manière multiplicative avec l’état dans une équation différentielle, il peut stabiliser ou déstabiliser le système, ce qui n’est pas le cas lorsque le bruit intervient de manière additive. Il y a plusieurs types de stabilité pour les systèmes décrits par des équations différentielles stochastiques, certaines étant plus pessimistes que d’autres. Dans ce manuscrit, nous avons cherché à relaxer les conditions de stabilité utilisées dans la littérature en employant la stabilité exponentielle presque sûre, aussi appelée stabilité exponentielle avec une probabilité de un. Trois domaines principaux sont traités dans ce manuscrit :(i) synthèse d’observateurs, (ii) commande des systèmes stochastiques,(iii) lemme borné réel pour les systèmes stochastiques algébro-différentiels.Un nouveau théorème sur la stabilité exponentielle presque sûre du point d’équilibre d’une classe de systèmes stochastiques non linéaires triangulaires est proposé : la stabilité de l’ensemble du système est assurée par la stabilité de chaque sous-système considéré isolément. La preuve de ce résultat est basée sur la majoration des exposants de Lyapunov. On a montré que le problème du filtrage des systèmes stochastiques avec des bruits multiplicatifs en imposant la stabilité exponentielle presque sûre de l’erreur d’observation ne peut pas être résolu en appliquant les approches de type Lyapunov disponibles dans la littérature. Cette difficulté a été surmontée en proposant d’exploiter la structure triangulaire associée à ce problème de filtrage, ce qui nous a permis de décomposer la synthèse de l’observateur en deux sous-problèmes découplés : (i) démontrer la stabilité de l’équation différentielle stochastique décrivant la dynamique de l’état à estimer, (ii) stabiliser l’équation différentielle stochastique décrivant la dynamique de l’erreur d’observation. Cette approche est basée sur le nouveau théorème sur la stabilité exponentielle presque sûre d’une classe de systèmes stochastiques non linéaires triangulaires et lipschitziens évoquée ci- dessus. Ce résultat a été étendu aux systèmes stochastiques non linéaires ayant des non linéarités de type one-sided Lipschitz. Pour garantir la stabilité de l’erreur d’observation, une approche de type polytopique a été proposée avec un formalisme “descripteur” (ou algébro-différentiel). Les résultats présentés ci-dessus ont été étendus à la synthèse d’observateurs robustes en présence d’incertitudes paramétriques. Des conditions pour le rejet asymptotique des perturbations intervenant dans une équation différen- tielle stochastique avec des bruits multiplicatifs ont été proposées. La stabilité considérée est la stabilité exponentielle presque sûre. Une borne de l’exposant de Lyapunov permet de garantir le taux de conver- gence vers zéro de l’état du système. Un correcteur de type bang-bang est synthétisé pour une classe de systèmes non linéaires stochastiques dans deux cas : (i) par retour d’état et (ii) par retour de sorties mesurées avec un observateur. Le type de stabilité utilisé est la stabilité exponentielle presque sûre. Une version du lemme borné réel est élaborée pour les systèmes stochastiques algébro-différentiels (ou singuliers, ou descripteurs) avec des bruits multiplicatifs. Ce travail a nécessité le développement de la formule d’Itô dans le cas des équations stochastiques algébro-différentielles non linéaires. Cette approche a été utilisée pour la synthèse d’un correcteur H∞ par retour de sorties en utilisant la stabilité exponentielle en moyenne quadratique. Un observateur pour les systèmes stochastiques algébro-différentiels non linéaires a été proposé avec la stabilité exponentielle presque sûre