Uri Shaked - Böcker

Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems begins with an introduction and extensive literature survey. The text proceeds to cover the field of H∞ time-delay linear systems where the issues of stability and L2−gain are presented and solved for nominal and uncertain stochastic systems, via the input-output approach. It presents solutions to the problems of state-feedback, filtering, and measurement-feedback control for these systems, for both the continuous- and the discrete-time settings. In the continuous-time domain, the problems of reduced-order and preview tracking control are also presented and solved. The second part of the monograph concerns non-linear stochastic state- multiplicative systems and covers the issues of stability, control and estimation of the systems in the H∞ sense, for both continuous-time and discrete-time cases. The book also describes special topics such as stochastic switched systems with dwell time and peak-to-peak filtering of nonlinear stochastic systems. The reader is introduced to six practical engineering- oriented examples of noisy state-multiplicative control and filtering problems for linear and nonlinear systems. The book is rounded out by a three-part appendix containing stochastic tools necessary for a proper appreciation of the text: a basic introduction to stochastic control processes, aspects of linear matrix inequality optimization, and MATLAB codes for solving the L2-gain and state-feedback control problems of stochastic switched systems with dwell-time. Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems will be of interest to engineers engaged in control systems research and development, to graduate students specializing in stochastic control theory, and to applied mathematicians interested in control problems. The reader is expected to have some acquaintance with stochastic control theory and state-space-based optimal control theory andmethods for linear and nonlinear systems.

Multiplicative noise appears in systems where the process or measurement noise levels depend on the system state vector. Such systems are relevant, for example, in radar measurements where larger ranges involve higher noise level.This monograph embodies a comprehensive survey of the relevant literature with basic problems being formulated and solved by applying various techniques including game theory, linear matrix inequalities and Lyapunov parameter-dependent functions.Topics covered include:? convex H2 and H-infinity norms analysis of systems with multiplicative noise; ? state feedback control and state estimation of systems with multiplicative noise; ? dynamic and static output feedback of stochastic bilinear systems; ? tracking controllers for stochastic bilinear systems utilizing preview information. Various examples which demonstrate the applicability of the theory to practical control engineering problems are considered; two such examples are taken from the aerospace and guidance control areas.

Advances in H∞ Control Theory is concerned with state-of-the-art developments in three areas:the extended treatment of mostly deterministic switched systems with dwell-time;the control of retarded stochastic state-multiplicative noisy systems; anda new approach to the control of biochemical systems, exemplified by the threonine synthesis and glycolytic pathways.Following an introduction and extensive literature survey, each of these major topics is the subject of an individual part of the book.The first two parts of the book contain several practical examples taken from various fields of control engineering including aircraft control, robot manipulation and process control. These examples are taken from the fields of deterministic switched systems and state-multiplicative noisy systems.The text is rounded out with short appendices covering mathematical fundamentals: σ-algebra and the input-output method for retarded systems.Advances in H∞ Control Theory is written for engineers engaged in control systems research and development, for applied mathematicians interested in systems and control and for graduate students specializing in stochastic control.