Impulsive Systems On Hybrid Time Domains
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Impulsive Systems on Hybrid Time Domains
This monograph discusses the issues of stability and the control of impulsive systems on hybrid time domains, with systems presented on discrete-time domains, continuous-time domains, and hybrid-time domains (time scales). Research on impulsive systems has recently attracted increased interest around the globe, and significant progress has been made in the theory and application of these systems. This book introduces recent developments in impulsive systems and fundamentals of various types of differential and difference equations. It also covers studies in stability related to time delays and other various control applications on the different impulsive systems. In addition to the analyses presented on dynamical systems that are with or without delays or impulses, this book concludes with possible future directions pertaining to this research.
Optimal Control of Dynamic Systems Driven by Vector Measures
This book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered. In the past few decades, there have been remarkable advances in the field of systems and control theory thanks to the unprecedented interaction between mathematics and the physical and engineering sciences. Recently, optimal control theory for dynamic systems driven by vector measures has attracted increasing interest. This book presents this theory for dynamic systems governed by both ordinary and stochastic differential equations, including extensive results on the existence of optimal controls and necessary conditions for optimality. Computational algorithms are developed based on the optimality conditions, with numerical results presented to demonstrate the applicability of the theoretical results developed in the book. This book will be of interest to researchers in optimal control or applied functional analysis interested in applications of vector measures to control theory, stochastic systems driven by vector measures, and related topics. In particular, this self-contained account can be a starting point for further advances in the theory and applications of dynamic systems driven and controlled by vector measures.
H-Systems
This book focuses on the observability of hybrid systems. It enables the reader to determine whether and how a hybrid system’s state can be reconstructed from sometimes necessarily partial information. By explaining how available measurements can be used to deduce past and future behaviours of a system, the authors extend this study of observability to embrace the properties of diagnosability and predictability. H-systems shows how continuous and discrete dynamics and their interaction affect the observability of this general class of hybrid systems and demonstrates that hybrid characteristics are not simply generalizations of well-known aspects of traditional dynamics. The authors identify conditions for state reconstruction, prediction and diagnosis of the occurrence of possibly faulty states. The formal approach to proving those properties for hybrid systems is accompanied by simple illustrative examples. For readers who are interested in the use of state estimation for controller design, the book also provides design methods for hybrid state observers and covers their application in some industrial cases. The book’s tutorial approach to the various forms of observability of hybrid systems helps to make H-systems of interest to academic researchers and graduate students working in control and to practitioners using control in an industrial environment.