Stabilization Problems with Constraints:

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.

Professor Smirnov is from the Moscow Physical-Technical Institute and he is presently based in the Mathematics Department at the University of Evora in Portugal Professor Bushenkov is based at the Computing Center of the Russian Academy of Sciences in Moscow

Preface	p. 5
Introduction	p. 7
Foundations	p. 13
Convex Analysis	p. 15
Convex sets	p. 15
Convex functions	p. 25
Differential properties of convex functions	p. 35
Set-valued maps	p. 42
Convex programming	p. 51
Differential equations and control systems	p. 57
Background notes	p. 57
Differential equations with discontinuous right-hand side	p. 59
Stability	p. 63
Lyapunov functions for linear systems	p. 68
Stability at first approximation	p. 71
Lyapunov's direct method for discrete systems	p. 74
Control systems	p. 78
Computational methods of convex analysis	p. 91
Polyhedral sets	p. 91
Polyhedral sets: computational aspects	p. 101
Numerical methods of convex programming	p. 106
Local Stabilization Problems	p. 117
Stabilization problem	p. 119
Statement of the problem	p. 119
The first approximation	p. 124
Stabilization of nonlinear systems	p. 132
Weak asymptotic stability and stabilizability	p. 140
Numerical algorithms	p. 143
Examples	p. 147
Controllable linear systems	p. 157
Controllability of linear systems	p. 157
Regulator design under controllability condition	p. 162
Single-input control systems	p. 166
The "peak" effect	p. 169
Optimality of transient characteristics	p. 174
Stabilization of uncertain systems	p. 181
Stabilization problems for uncertain systems	p. 181
Numerical experiments	p. 185
Unilateral stabilization	p. 191
Statement of the problem	p. 191
The case of linear control system	p. 194
Unilateral stabilization for a nonlinear system	p. 201
Stabilization with state constraints	p. 207
Computational algorithms and examples	p. 210
Nonlocal Stabilization Problems	p. 217
Stabilization to sets	p. 219
Stabilization of a linear system to a convex cone	p. 219
Stabilization to a surface	p. 226
Discrete-time stabilization problem	p. 233
Stabilization of periodic systems	p. 238
Computational algorithms and examples	p. 248
Global stabilization problem	p. 257
Guidance control	p. 257
The guide design problem	p. 259
Global guidance stabilizers for linear systems	p. 263
Global stabilizers for linear systems	p. 265
Guidance stabilization of nonlinear systems, I	p. 268
Guidance stabilization of nonlinear systems, II	p. 271
Application to differential games	p. 278
Numerical experiments	p. 279
Comments	p. 287
Bibliography	p. 291
Index	p. 297
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Stabilization Problems with Constraints: Analysis and Computational Aspects

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