Format:
Online Ressource (xiv, 252 pages)
Edition:
Online-Ausg.
ISBN:
9780080955896
,
0080955894
,
9780121189501
Series Statement:
Mathematics in science and engineering v. 81
Uniform Title:
P@rogrammation dynamique et ses applications 〈English〉
Content:
Pt. I. Discrete deterministic processes. The principles of dynamic programming -- Processes with bounded horizon -- Processes with infinite or unspecified horizon -- Practical solution of the optimal recurrence relation -- pt. II. Discrete random processes. General theory -- Processes with discrete states -- pt. III. Numerical synthesis of the optimal controller for a linear process. General discussion of the problem -- Numerical optimal control of a measurable deterministic process -- Numerical optimal control of a stochastic process -- pt. IV. Continuous processes. Continuous deterministic processes -- Continuous stochastic processes -- pt. V. Applications. Introductory example -- Minimum use of control effort in a first-order system -- Optimal tabulation of functions -- Regulation of angular position with minimization of a quadratic criterion -- Control of a stochastic system -- Minimum-time depth change of a submersible vehicle -- Optimal interception -- Control of a continuous process -- Filtering.
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 matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory and its particular branches, such as optimal filtering and information compression
Note:
Includes bibliographical references. - Print version 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
,
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
,
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
,
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
,
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
Additional Edition:
ISBN 0121189503
Additional Edition:
Erscheint auch als Druck-Ausgabe Boudarel, R. (René) Dynamic programming and its application to optimal control New York, Academic Press, 1971
Language:
English
Keywords:
Optimale Kontrolle
;
Dynamische Optimierung
;
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;
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