This book deals with two aspects of the optimal control of oscillatory systems: the initiation of optimal oscillatory regimes and possibilities of the control for random disturbances. The main content of the book is based on some assertions of the optimal control theory and the disturbance theory. Informations necessary for the understanding are given in the appendix. All the theoretical propositions are illustrated by examples with exact mechanical context. Since the book mainly contains mathematical foundations, applications are not limited to the given examples.
Introduction
Chapter 1 : Optimal Periodic Control. The Integral Equations Method
Chapter 2 : Periodic Control for Vibroimpact Systems
Chapter 3 : The Averaging Method in Oscillation Control Problems
Chapter 4 : Oscillations in Systems with Random Disturbances
Chapter 5 : Some Problems of Optimal Control for Systems with Random Disturbances
A Appendix
A.1 : Pontryagin Maximum Principle
A.2 : Disturbances in Optimal Systems
A.3 : Main Theorems of the Averaging Method
A.4 : Necessary Condition of the Optimality of Periodic Regimes
A.5 : Maximum Principle for Stochastic Equations with Program Control
A.6 : Main Theorems of Diffusion Approximation Method
References
