The authors present a study of the H-infinity control problem and related topics for descriptor systems, described by a set of nonlinear differential-algebraic equations. They derive necessary and sufficient conditions for the existence of a controller solving the standard nonlinear H-infinity control problem considering both state and output feedback. One such condition for the output feedback control problem to be solvable is obtained in terms of Hamilton–Jacobi inequalities and a weak coupling condition; a parameterization of output feedback controllers solving the problem is also provided. All of these results are then specialized to the linear case. The derivation of state-space formulae for all controllers solving the standard H-infinity control problem for descriptor systems is proposed. Among other important topics covered are balanced realization, reduced-order controller design and mixed H2/H-infinity control. "H-infinity Control for Nonlinear Descriptor Systems" provides a comprehensive introduction and easy access to advanced topics.

H-infinity control made considerable strides toward systematizing classical control. This bookaddresses how this extends to nonlinear systems.

A comprehensive overview of nonlinear H∞ control theory for both continuous-time and discrete-time systems, Nonlinear H∞-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear H∞-control, nonlinear H∞ -filtering, mixed H2/ H∞-nonlinear control and filtering, nonlinear H∞-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter. Recent progress in developing computational schemes for solving the Hamilton-Jacobi equation (HJE) has facilitated the application of Hamilton-Jacobi theory in both mechanics and control. As there is currently no efficient systematic analytical or numerical approach for solving them, the biggest bottle-neck to the practical application of the nonlinear equivalent of the H∞-control theory has been the difficulty in solving the Hamilton-Jacobi-Isaacs partial differential-equations (or inequalities). In light of this challenge, the author hopes to inspire continuing research and discussion on this topic via examples and simulations, as well as helpful notes and a rich bibliography. Nonlinear H∞-Control, Hamiltonian Systems and Hamilton-Jacobi Equations was written for practicing professionals, educators, researchers and graduate students in electrical, computer, mechanical, aeronautical, chemical, instrumentation, industrial and systems engineering, as well as applied mathematics, economics and management.

Chapter headings and selected papers: Controller Design for Nonlinear Systems. Global regulation problem for nonlinear systems (S.M. Fei, C.-B. Feng). Sliding Mode Control of Nonlinear Systems. Nonlinear sliding surface design in the presence of uncertainty (A. Loukianov et al.). H-Infinity and Nonlinear Control. Control of nonlinear systems via feedback linearization and constrained model predictive control (W.-K. Son, O.K. Kwon). Optimization and Related Topics I. Optimization of boundary and starting controls in multi-dimensional hyperbolic systems (A.V. Arguchintsev). Optimization and Related Topics II. The optimal stabilization of plasma under uncertainty conditions (V.F. Gubarev, O.S. Yakovlev). Advanced Applications of Genetic Algorithms. Multidisciplinary optimization with evolutionary computing for control design (W. Khatib et al.). Linear Quadratic Optimal Control. Singular optimal control problem of linear singular systems with linear-quadratic cost (Y. Chen et al.). Control Applications of Optimization. The optimal control of processing systems by economical criteria as applied to distillation (V.P. Krivosheev, A.Y. Torgashov). Optimal Control I. Stability properties of an iterative optimal control algorithm (P.D. Roberts). Optimal Control II. Quadratic index analysis in predictive control (J.S. Senent et al.). H-Infinity Control and Game Theoretical Approach. Game problem of approach under failure of controlling devices (A.A. Chikrii). Optimal Control Design. The Yakubovich-Kalman-Popov lemma and stability analysis of dynamic output feedback systems (R. Johansson, A. Robertsson). Nonlinear Robust Control I. Robust stability of uncertain systems with differentiable nonlinearity (A. Gaiduk). Nonlinear Robust Control II. Robust nonlinear forwarding with smooth state feedback control (W.Z. Su, M. Fu). Optimal, Robust Control I. Robust reliable H∞ controllers design via LMIS (D. Hu, W.-H. Chen). Optimal, Robust Control II. A dynamic games approach to disturbance attenuation control of discrete-time descriptor systems (H. Xu). Author index. Keyword index.

Chapter headings and selected papers: Controller Design for Nonlinear Systems. Global regulation problem for nonlinear systems (S.M. Fei, C.-B. Feng). Sliding Mode Control of Nonlinear Systems. Nonlinear sliding surface design in the presence of uncertainty (A. Loukianov et al.). H-Infinity and Nonlinear Control. Control of nonlinear systems via feedback linearization and constrained model predictive control (W.-K. Son, O.K. Kwon). Optimization and Related Topics I. Optimization of boundary and starting controls in multi-dimensional hyperbolic systems (A.V. Arguchintsev). Optimization and Related Topics II. The optimal stabilization of plasma under uncertainty conditions (V.F. Gubarev, O.S. Yakovlev). Advanced Applications of Genetic Algorithms. Multidisciplinary optimization with evolutionary computing for control design (W. Khatib et al.). Linear Quadratic Optimal Control. Singular optimal control problem of linear singular systems with linear-quadratic cost (Y. Chen et al.). Control Applications of Optimization. The optimal control of processing systems by economical criteria as applied to distillation (V.P. Krivosheev, A.Y. Torgashov). Optimal Control I. Stability properties of an iterative optimal control algorithm (P.D. Roberts). Optimal Control II. Quadratic index analysis in predictive control (J.S. Senent et al.). H-Infinity Control and Game Theoretical Approach. Game problem of approach under failure of controlling devices (A.A. Chikrii). Optimal Control Design. The Yakubovich-Kalman-Popov lemma and stability analysis of dynamic output feedback systems (R. Johansson, A. Robertsson). Nonlinear Robust Control I. Robust stability of uncertain systems with differentiable nonlinearity (A. Gaiduk). Nonlinear Robust Control II. Robust nonlinear forwarding with smooth state feedback control (W.Z. Su, M. Fu). Optimal, Robust Control I. Robust reliable H∞ controllers design via LMIS (D. Hu, W.-H. Chen). Optimal, Robust Control II. A dynamic games approach to disturbance attenuation control of discrete-time descriptor systems (H. Xu). Author index. Keyword index.

This book provides techniques to produce robust, stable and useable solutions to problems of H-infinity and H2 control in high-performance, non-linear systems for the first time. The book is of importance to control designers working in a variety of industrial systems. Case studies are given and the design of nonlinear control systems of the same caliber as those obtained in recent years using linear optimal and bounded-norm designs is explained.

Takagi-Sugeno Fuzzy Systems Non-fragile H-infinity Filtering investigates the problem of non-fragile H-infinity filter design for Takagi-Sugeno (T-S) fuzzy systems. Given a T-S fuzzy system, the objective of this book is to design an H-infinity filter with the gain variations such that the filtering error system guarantees a prescribed H-infinity performance level. Furthermore, it demonstrates that the solution of non-fragile H-infinity filter design problem can be obtained by solving a set of linear matrix inequalities (LMIs). The intended audiences are graduate students and researchers both from the fields of engineering and mathematics. Dr. Xiao-Heng Chang is an Associate Professor at the College of Engineering, Bohai University, Jinzhou, Liaoning, China.

This book discusses systematic designs of stable adaptive fuzzy logic controllers employing hybridizations of Lyapunov strategy-based approaches/H∞ theory-based approaches and contemporary stochastic optimization techniques. The text demonstrates how candidate stochastic optimization techniques like Particle swarm optimization (PSO), harmony search (HS) algorithms, covariance matrix adaptation (CMA) etc. can be utilized in conjunction with the Lyapunov theory/H∞ theory to develop such hybrid control strategies. The goal of developing a series of such hybridization processes is to combine the strengths of both Lyapunov theory/H∞ theory-based local search methods and stochastic optimization-based global search methods, so as to attain superior control algorithms that can simultaneously achieve desired asymptotic performance and provide improved transient responses. The book also demonstrates how these intelligent adaptive control algorithms can be effectively utilized in real-life applications such as in temperature control for air heater systems with transportation delay, vision-based navigation of mobile robots, intelligent control of robot manipulators etc.