Dynamic programming and stochastic control / Dimitri P. Bertsekas.

Format:

Book

Author/Creator:

Bertsekas, Dimitri P.

Series:

Mathematics in science and engineering ; v. 125.

Mathematics in science and engineering ; v. 125

Language:

English

Subjects (All):

Dynamic programming.

Stochastic processes.

Physical Description:

1 online resource (415 p.)

Place of Publication:

New York : Academic Press, 1976.

Language Note:

English

Summary:

Dynamic programming and stochastic control

Contents:

Front Cover; Dynamic Programming and Stochastic Control; Copyright Page; Contents; Preface; Acknowledgments; Chapter 1. Introduction; 1.1 The Problems of Decision under Uncertainty; 1.2 Expected Utility Theory and Risk; 1.3 Some Nonsequential Decision Problems; 1.4 A Model for Sequential Decision Making; 1.5 Notes; Problems; Part I: CONTROL OF UNCERTAIN SYSTEMS OVER A FINITE HORIZON; Chapter 2. The Dynamic Programming Algorithm; 2.1 The Basic Problem; 2.2 The Dynamic Programming Algorithm; 2.3 Time Lags, Correlated Disturbances, and Forecasts; 2.4 Notes; Problems

Chapter 3. Applications in Specific Areas3.1 Linear Systems with Quadratic Cost Functional-The Certainty Equivalence Principle; 3.2 Inventory Control; 3.3 Dynamic Portfolio Analysis; 3.4 Optimal Stopping Problems-Examples; 3.5 Notes; Problems; Chapter 4. Problems with Imperfect State Information; 4.1 Reduction to the Perfect State Information Case; 4.2 Sufficient Statistics; 4.3 Linear Systems with Quadratic Cost Functionals-Separation of Estimation and Control; 4.4 Finite State Markov Chains-A Problem of Instruction; 4.5 Hypothesis Testing-Sequential Probability Ratio Test

4.6 Sequential Sampling of a Large Batch4.7 Notes; Problems; Appendix. Least-Squares Estimation-The Kalman Filter; Chapter 5. Computational Aspects of Dynamic Programming-Suboptimal Control; 5.1 The Curse of Dimensionality; 5.2 Discretization Procedures and Their Convergence; 5.3 Suboptimal Controllers and the Notion of Adaptivity; 5.4 Naive Feedback and Open-Loop Feedback Controllers; 5.5 Partial Open-Loop Feedback Controllers and the Efficient Utilization of Forecasts; 5.6 Control of Systems with Unknown Parameters-Self-Tuning Regulators; 5.7 Notes; Problems

Part II: CONTROL OF UNCERTAIN SYSTEMS OVER AN INFINITE HORIZONChapter 6. Minimization of Total Expected Value-Discounted Cost; 6.1 Convergence and Existence Results; 6.2 Computational Methods-Successive Approximation, Policy Iteration, Linear Programming; 6.3 Contraction Mappings; 6.4 Unbounded Costs per Stage; 6.5 Linear Systems and Quadratic Cost Functionals; 6.6 Inventory Control; 6.7 Nonstationary and Periodic Problems; 6.8 Notes; Problems; Chapter 7. Minimization of Total Expected Value-Undiscounted Cost; 7.1 Convergence and Existence Results; 7.2 Optimal Stopping

7.3 Optimal Gambling Strategies7.4 The First Passage Problem; 7.5 Notes; Problems; Chapter 8. Minimization of Average Expected Value; 8.1 Existence Results; 8.2 Successive Approximation; 8.3 Policy Iteration; 8.4 Infinite State Space-Linear Systems with Quadratic Cost Functionals; 8.5 Notes; Problems; Appendix. Existence Analysis under the Weak Accessibility Condition; APPENDIXES; Appendix A. Mathematical Review; Appendix B. On Optimization Theory; Appendix C. On Probability Theory; Appendix D. On Finite State Markov Chains; References; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-282-28923-3

9786612289231

0-08-095634-3

OCLC:

466442585