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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.
Preface
Introduction
Foundations
Convex Analysis
Convex sets
Convex functions
Differential properties of convex functions
Set-valued maps
Convex programming
Differential equations and control systems
Background notes
Differential equations with discontinuous right-hand side
Stability
Lyapunov functions for linear systems
Stability at first approximation
Lyapunov's direct method for discrete systems
Control systems
Computational methods of convex analysis
Polyhedral sets
Polyhedral sets: computational aspects
Numerical methods of convex programming
Local Stabilization Problems
Stabilization problem
Statement of the problem
The first approximation
Stabilization of nonlinear systems
Weak asymptotic stability and stabilizability
Numerical algorithms
Examples
Controllable linear systems
Controllability of linear systems
Regulator design under controllability condition
Single-input control systems
The "peak" effect
Optimality of transient characteristics
Stabilization of uncertain systems
Stabilization problems for uncertain systems
Numerical experiments
Unilateral stabilization
Statement of the problem
The case of linear control system
Unilateral stabilization for a nonlinear system
Stabilization with state constraints
Computational algorithms and examples
Nonlocal Stabilization Problems
Stabilization to sets
Stabilization of a linear system to a convex cone
Stabilization to a surface
Discrete-time stabilization problem
Stabilization of periodic systems
Computational algorithms and examples
Global stabilization problem
Guidance control
The guide design problem
Global guidance stabilizers for linear systems
Global stabilizers for linear systems
Guidance stabilization of nonlinear systems, I
Guidance stabilization of nonlinear systems, II
Application to differential games
Numerical experiments
Comments
Bibliography
Index