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

Cover......Page 1
Half Title......Page 2
Series Page......Page 4
Title Page......Page 8
Copyright Page......Page 9
Preface......Page 10
Contents......Page 16
Introduction......Page 18
 1.1. Statement of synthesis problems for optimal control systems......Page 24
 1.2. Differential equationa for controlled systems with random functions......Page 49
 1.3. Deterministic control problems. Formal scheme of the dynamic programming approach......Page 65
 1.4. The Bellman equations for Markov controlled processes......Page 74
 1.5. Sufficient coordinates in control problems with indirect observations......Page 92
 2.1. Linear-quadratic problems of optimal control (LQ-problems)......Page 110
 2.2. Problem of optimal tracking a wandering coordinate......Page 120
 2.3. Optimal control of the population size......Page 140
 2.4. Stochastic problem of optimal fisheries management......Page 150
Chapter III. Approximate Synthesis of Stochastic Control Systems With Small Control Actions......Page 158
 3.1. Approximate solution of stationary synthesis problems......Page 161
 3.2. Calculation of a quasioptimal regulator for the oscillatory plant......Page 171
 3.3. Synthesis of quasioptimal controls in the case of correlated noises......Page 181
 3.4. Noostatiooary problems. Estimates of the quality of approximate synthesis......Page 192
 3.5. Analysis of the asymptotic convergence of successive approximations (3.0.6)-(3.0.8) as k → ∞......Page 205
 3.6. Approximate synthesis of some stochastic systems with distributed parameters......Page 216
Chapter IV. Synthesis of Quasioptimal Systems in the Case of Small Diffusion Terms in the Bellman Equation......Page 236
 4.1. Approximate synthesis of a servomechanism with small-intensity noise......Page 238
 4.2. Calculation of a quasioptimal system for tracking a discrete Markov process......Page 250
Chapter V. Control of Oscillatory Systems......Page 264
 5.1. Optimal control of a quasiharmonic oscillator. An asymptotic synthesis method......Page 265
 5.2. Control of the \"predator-prey\" system. The case of a poorly adapted predator......Page 284
 5.3. Optimal damping of random oscillations......Page 293
 5.4. Optimal control of quasiharmonic systems with noise in the feedback circuit......Page 315
Chapter VI. Some Special Applications of Asymptotic Synthesis Methods......Page 328
 6.1. Adaptive problems of optimal control......Page 329
 6.2. Some stochastic control problems with constrained phase coordinates......Page 345
 6.3. Optimal control of the population size governed by the stochastic logistic model......Page 358
Chapter VII. Numerical Synthesis Methods......Page 372
 7.1. Numerical solution of the problem of optimal damping of random oscillations......Page 373
 7.2. Optimal control for the \"predator-prey\" system (the general case)......Page 385
Conclusion......Page 400
References......Page 404
Index......Page 418