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Variational methods in optimum control theory
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Variational methods in optimum control theory
| Title |
Variational methods in optimum control theory / Iu. P. Petrov. Translated by M. D. Friedman with the assistance of H. J. ten Zeldam. |
|---|---|
| Publisher |
New York : Academic Press |
| Creation Date |
1968 |
| Notes |
Description based upon print version of record. Includes bibliographical references and index. English |
| Content |
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 |
| Series |
Mathematics in science and engineering 45 |
| Extent |
1 online resource (231 p.) |
| Language |
English |
| National Library system number |
997010718458105171 |
MARC RECORDS
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