Optimal Design of Control Systems: Stochastic and Deterministic Problems (Pure and Applied Mathematics: A Series of Monographs and Textbooks/221)

by Kolosov; Gennadii E.

• ISBN13: 9780824775377
• ISBN10: 0824775376
• Edition: 1st
• Format: Hardcover
• Copyright: 1999-06-01
• Publisher: CRC Press

Summary

Covers design methods for optimal control algorithms in the form of synthesis for deterministic and stochastic dynamical systems, with applications to biological, radio engineer- ing, mechanical, and servomechanical technologies. DLC: Control theory.

Table of Contents

Preface	v
Introduction	1	(6)
Synthesis Problems for Control Systems and the Dynamic Programming Approach	7	(86)
Statement of synthesis problems for optimal control systems	7	(25)
Differential equations for controlled systems with random functions	32	(16)
Deterministic control problems. Formal scheme of the dynamic programming approach	48	(9)
The Bellman equations for Markov controlled processes	57	(18)
Sufficient coordinates in control problems with indirect observations	75	(18)
Exact Methods for Synthesis Problems	93	(48)
Linear-quadratic problems of optimal control (LQ-problems)	93	(10)
Problem of optimal tracking a wandering coordinate	103	(20)
Optimal control of the population size	123	(10)
Stochastic problem of optimal fisheries management	133	(8)
Approximate Synthesis of Stochastic Control Systems With Small Control Actions	141	(78)
Approximate solution of stationary synthesis problems	144	(10)
Calculation of a quasioptimal regulator for the oscillatory plant	154	(10)
Synthesis of quasioptimal controls in the case of correlated noises	164	(11)
Nonstationary problems. Estimates of the quality of approximate synthesis	175	(13)
Analysis of the asymptotic convergence of successive approximations (3.0.6)-(3.0.8) as k → ∞	188	(11)
Approximate synthesis of some stochastic systems with distributed parameters	199	(20)
Synthesis of Quasioptimal Systems in the Case of Small Diffusion Terms in the Bellman Equation	219	(28)
Approximate synthesis of a servomechanism with small-intensity noise	221	(12)
Calculation of a quasioptimal system for tracking a discrete Markov process	233	(14)
Control of Oscillatory Systems	247	(64)
Optimal control of a quasiharmonic oscillator. An asymptotic synthesis method	248	(19)
Control of the ``predator--prey'' system. The case of a poorly adapted predator	267	(9)
Optimal damping of random oscillations	276	(22)
Optimal control of quasiharmonic systems with noise in the feedback circuit	298	(13)
Some Special Applications of Asymptotic Synthesis Methods	311	(44)
Adaptive problems of optimal control	312	(16)
Some stochastic control problems with constrained phase coordinates	328	(13)
Optimal control of the population size governed by the stochastic logistic model	341	(14)
Numerical Synthesis Methods	355	(28)
Numerical solution of the problem of optimal damping of random oscillations	356	(12)
Optimal control for the ``predator--prey'' system (the general case)	368	(15)
Conclusion	383	(4)
References	387	(14)
Index	401