Description

Book Synopsis
This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.

Table of Contents
I. Calculus of Variations.- 1. Introduction.- 2. Problem Statement and Necessary Conditions for an Extremum.- 3. Integration of the Euler—Lagrange Equation.- 4. An Inverse Problem.- 5. The Weierstrass Necessary Condition.- 6. Jacobi’s Necessary Condition.- 7. Corner Conditions.- 8. Concluding Remarks.- II. Optimal Control.- 9. Introduction.- 10. Problem Statement and Optimality.- 11. Regular Optimal Trajectories.- 12. Examples of Extremal Control.- 13. Some Generalizations.- 14. Special Systems.- 15. Sufficient Conditions.- 16. Feedback Control.- 17. Optimization with Vector-Valued Cost.- References.

The Calculus of Variations and Optimal Control An Introduction Mathematical Concepts And Methods In Science And Engineering 24

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      View other formats and editions of The Calculus of Variations and Optimal Control An Introduction Mathematical Concepts And Methods In Science And Engineering 24 by George Leitmann

      Publisher: Springer Us
      Publication Date: 5/23/2013 12:00:00 AM
      ISBN13: 9781489903358, 978-1489903358
      ISBN10: 1489903356

      Description

      Book Synopsis
      This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.

      Table of Contents
      I. Calculus of Variations.- 1. Introduction.- 2. Problem Statement and Necessary Conditions for an Extremum.- 3. Integration of the Euler—Lagrange Equation.- 4. An Inverse Problem.- 5. The Weierstrass Necessary Condition.- 6. Jacobi’s Necessary Condition.- 7. Corner Conditions.- 8. Concluding Remarks.- II. Optimal Control.- 9. Introduction.- 10. Problem Statement and Optimality.- 11. Regular Optimal Trajectories.- 12. Examples of Extremal Control.- 13. Some Generalizations.- 14. Special Systems.- 15. Sufficient Conditions.- 16. Feedback Control.- 17. Optimization with Vector-Valued Cost.- References.

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