Stabilization Problems with Constraints: Analysis and Computational Aspects

Description

Presents and demonstrates stabilizer design techniques that can be used to solve stabilization problems with constraints. These methods have their origins in convex programming and stability theory. However, to provide a practical capability in stabilizer design, the methods are tailored to the special features and needs of this field. Hence, the main emphasis of this book is on the methods of stabilization, rather than optimization and stability theory. The text is divided into three parts. Part I contains some background material. Part II is devoted to behavior of control systems, taking examples from mechanics to illustrate the theory. Finally, Part III deals with nonlocal stabilization problems, including a study of the global stabilization problem. Cover Half Title Title Page Copyright Page Table of Contents Preface Introduction I Foundations 1 Convex Analysis 1.1 Convex sets 1.2 Convex functions 1.3 Differential properties of convex functions 1.4 Set-valued maps 1.5 Convex programming 2 Differential equations and control systems 2.1 Background notes 2.2 Differential equations with discontinuous right-hand side 2.3 Stability 2.4 Lyapunov functions for linear systems 2.5 Stability at first approximation 2.6 Lyapunov's direct method for discrete systems 2.7 Control systems 3 Computational methods of convex analysis 3.1 Polyhedral sets 3.2 Polyhedral sets: computational aspects 3.3 Numerical methods of convex programming II Local Stabilization Problems 4 Stabilization problem 4.1 Statement of the problem 4.2 The first approximation 4.3 Stabilization of nonlinear systems 4.4 Weak asymptotic stability and stabilizability 4.5 Numerical algorithms 4.6 Examples 5 Controllable linear systems 5.1 Controllability of linear systems 5.2 Regulator design under controllability condition 5.3 Single-input control systems 5.4 The "peak" effect 5.5 Optimality of transient characteristics 6 Stabilization of uncertain systems 6.1 Stabilization problems for uncertain systems 6.2 Numerical experiments 7 Unilateral stabilization 7.1 Statement of the problem 7.2 The case of linear control system 7.3 Unilateral stabilization for a nonlinear system 7.4 Stabilization with state constraints 7.5 Computational algorithms and examples III Nonlocal Stabilization Problems 8 Stabilization to sets 8.1 Stabilization of a linear system to a convex cone 8.2 Stabilization to a surface 8.3 Discrete-time stabilization problem 8.4 Stabilization of periodic systems 8.5 Computational algorithms and examples 9 Global stabilization problem 9.1 Guidance control 9.2 The guide design problem 9.3 Global guidance stabilizers for linear systems 9.4 Global stabilizers for linear systems 9.5 Guidance stabilization of nonlinear systems, I 9.6 Guidance stabilization of nonlinear systems, II 9.7 Application to differential games 9.8 Numerical experiments Comments Bibliograph Index