Constrained Control Problems of Discrete Processes

The following sections are included:

• Preface

• Contents

The following sections are included:

• Discrete-time control systems

• Constrained control problems

• Statement of the problem

• Organization of the book

The following sections are included:

• Mathematical background

• Auxiliary results

The following sections are included:

• Linear stationary systems

• Linear nonstationary systems

• Linear descriptor systems

• Systems with multiple delays and perturbations

The following sections are included:

• Quasilinear discrete-time systems

• Convex set-valued processes

• Nonconvex set-valued processes

• 2-D Nonlinear control systems

• Nonsmooth control systems

The following sections are included:

• Discrete-time game

• Continuous-time control systems

• Stabilizability of control systems

• Discrete maximum principle and controllability

• Observability and controllability

In classical control theory, the algebraic and geometric approaches have been developed as a powerful tool for solving controllability problems. It no longer makes use of these approaches when typically constrained controllability is involved. In this book we have investigated constrained control problems of discrete processes and some of their applications using the functional analysis approach. In the main part of the work the controllability problem for linear and nonlinear discrete-time systems with constraints on both control and state has been considered. Necessary and sufficient conditions for constrained controllability, reachability, stabilizability have been established fruitfully by using the set-valued techniques. Although the results were mainly meant to be used in discrete-time, we were able to develop some of them for continuous-time systems based on similar ideas…

The following sections are included:

• Appendix
  • Banach spaces
  • Set-valued analysis
  • Elements of classical controllability theory
    • Controllability
    • Controllability and stabilizability

• Bibliography

• Notations

• Index