UID:
almahu_9947366253102882
Format:
1 online resource (271 p.)
ISBN:
1-283-52617-4
,
9786613838629
,
0-08-095589-4
Series Statement:
Mathematics in science and engineering ; v. 81
Uniform Title:
Programmation dynamique et ses applications.
Content:
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank
Note:
Description based upon print version of record.
,
Front Cover; Dynamic Programming and its Application to Optimal Control; Copyright Page; Contents; Foreword; Preface; PART 1: DISCRETE DETERMINISTIC PROCESSES; Chapter 1. The Principles of Dynamic Programming; 1.1 General Description of the Method; 1.2 Example of the General Method; 1.3 Sequential Decision Problems and the Principle of Optimality; 1.4 An Example of Application of the Principle of Optimality; 1.5 Remarks; Chapter 2. Processes with Bounded Horizon; 2.1 Definition of a Discrete Process; 2.2 Statement of the Problem; 2.3 Application of the Principle of Optimality
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2.4 Direct Derivation of the Recurrence Equation2.5 Analog Interpretation of the Recurrence Equation; 2.6 Practical Application of the Recurrence Equation; 2.7 Additive Constraints; 2.8 Sensitivity of the Solution; Chapter 3. Processes with Infinite or Unspecified Horizon; 3.1 Processes with Infinite Horizon; 3.2 Processes with Unspecified Horizon; 3.3 Structure and Stability of a System with Infinite Horizon; 3.4 Calculation of the Solution of the Optimality Equation; Chapter 4. Practical Solution of the Optimal Recurrence Relation; 4.1 Search for an Optimum
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4.2 The Problem of Dimensionality4.3 Domain of Definition of the Return Function; 4.4 Solution by Successive Approximations; 4.5 The Use of Legendre Polynomials; 4.6 Linear Systems with Quadratic Costs; 4.7 Linearization; 4.8 Reduction of the Dimensionality; PART 2: DISCRETE RANDOM PROCESSES; Chapter 5. General Theory; 5 .1 Optimal Control of Stochastic Processes; 5.2 Processes with Bounded Horizon and Measurable State; 5.3 Processes with Random Horizon and Measurable State; 5.4 Processes with a State Not Completely Measurable; 5.5 Conclusions; Chapter 6. Processes with Discrete States
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6.1 Fundamentals6.2 Terminal Problems; 6.3 Optimization of a Return Function; 6.4 Discrete Stochastic Processes with Discrete States Which Are Not Completely Measurable; PART 3: NUMERICAL SYNTHESIS OF THE OPTIMAL CONTROLLER FOR A LINEAR PROCESS; Chapter 7. General Discussion of the Problem; 7.1 Definition of the Problem; 7.2 Mathematical Models of the Units; 7.3 The Canonical Model; 7.4 The System Objective; 7.5 Problem Types; Chapter 8. Numerical Optimal Control of a Measurable Deterministic Process; 8.1 The Effect of Terminal Constraints; 8.2 Minimum-Time Regulation with Bounded Energy
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8.3 Problems with Quadratic Constraints8.4 The Case of an Infinite Horizon; Chapter 9. Numerical Optimal Control of a Stochastic Process; 9.1 Completely Measurable Processes; 9.2 The Case of Possible Missed Controls; 9.3 Processes with a State Not Completely Measurable; 9.4 Conclusions; PART 4: CONTINUOUS PROCESSES; Chapter 10. Continuous Deterministic Processes; 10.1 A Continuous Process as the Limit of a Discrete Process; 10.2 Establishment of the Functional Optimality Equations; 10.3 Special Case of Unconstrained Control; 10.4 Application to the Calculus of Variations
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10.5 The Maximum Principle
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English
Additional Edition:
ISBN 0-12-118950-3
Language:
English
