Variational methods in optimum control theory / Iu. P. Petrov. Translated by M. D. Friedman with the assistance of H. J. ten Zeldam.

Format:

Book

Author/Creator:

Petrov, IU. P.

Series:

Mathematics in science and engineering ; 45.

Mathematics in science and engineering ; 45

Language:

English

Subjects (All):

Control theory.

Calculus of variations.

Physical Description:

1 online resource (231 p.)

Place of Publication:

New York : Academic Press, 1968.

Language Note:

English

Summary:

Variational methods in optimum control theory

Contents:

Front Cover; Variational Methods in Optimum Control Theory; Copyright Page; Contents; From the Preface to the Russian Edition; Chapter I. Fundamental Concepts of the Calculus of Variations; 1. Functionals; 2. Admissible Lines. Function Classes; 3. Nearness of Functions; 4. Classification of Extremums; 5. Euler Equation; 6. Discussion of the Euler Equation; 7. The Legendre Condition; Chapter II. Generalizations of the Simplest Problem of Calculus of Variations; 8. Problems with Variable Endpoints. General Formula for the Variations; 9. Transversality Conditions

10. Extremals with Breaks. Weierstrass-Erdmann Conditions11. Functionals Dependent on Several Unknown Functions; 12. Functionals Dependent on Higher-Order Derivatives; 13. Conditional Extremum; 14. Isoperimetric Problem; 15. General Lagrange Problem. Maier and Bolza Problems; 16. Variational Problems in Parametric Form; 17. Canonical Form of the Euler Equations; 18. Extremum of a Functional Dependent on a Function of Several Variables; Chapter III. Applying the Euler Equation to the Solution of Engineering Problems; 19. Direct Current Electric Motor

20. Estimate of the Change in a Functional When the Actual Function Deviates from the Extremal21. Reciprocity Principle; Its Boundedness; 22. Selection of the Optimum Gear Ratio. Extremals with a Parameter; 23. Electric Load Driver with Time-Dependent Resistance Moment. Boundary Conditions at Infinity; 24. More General Problems of Optimum Control. Electric Drive with a Resistance Moment Dependent on the Velocity, and a Magnetic Flux Dependent on the Armature Current; Chapter IV. Field Theory. Sufficient Conditions for an Extremum; 25. Field of Extremals; 26. Jacobi and Legendre Conditions

27. Strong Extremum. Weierstrass Condition28. Summary of Necessary and Sufficient Conditions for an Extremum; 29. Degenerate Functionals; 30. The Work of V. F. Krotov; Chapter V. Extremum Problem with Constraints; 31. Problems with Constraints in Classical Calculus of Variations; 32. Linear Optimum Control Problems; 33. The Maximum Principle; 34. Synthesis of an Optimum Control; 35. Dynamic Programming; 36. Nonstandard Functionals; 37. Appropriate Methods of Solution; Chapter VI. Examples of the Application of Variational Methods

38. Optimum Control of DC Electric Motors with Velocity and Armature Current Constraints39. Control Assuring Minimum Rated Generator Power (Example with a Nonstandard Functional); 40. Control of a Compound with Independent Excitation in the Armature and Excitation Loops; 41. Control with a Voltage Constraint; 42. Determination of the Maximum Allowable Dynamic Effect; 43. Control of the Excitation of a Synchronous Machine Assuring the Highest Degree of Stability; 44. Optimum Control of Locomotive Motion; 45. Amplitude and Frequency Control of Asynchronous Electric Motors

Appendix I: Historical Survey

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-282-29044-4

9786612290442

0-08-095553-3

OCLC:

316573078