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A Primer on the Calculus of Variations and Optimal Control Theory

About this Title

Mike Mesterton-Gibbons, Florida State University, Tallahassee, FL

Publication: The Student Mathematical Library
Publication Year 2009: Volume 50
ISBNs: 978-0-8218-4772-5 (print); 978-1-4704-1635-5 (online)
DOI: http://dx.doi.org/10.1090/stml/050
MathSciNet review: MR2522971
MSC: Primary 49-01

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Table of Contents

Front/Back Matter

• View this volume's front and back matter

Chapters

• Lecture 1. The Brachistochrone
• Lecture 2. The fundamental problem. Extremals
• Lecture 3. The insufficiency of extremality
• Lecture 4. Important first integrals
• Lecture 5. The du Bois-Reymond equation
• Lecture 6. The corner conditions
• Lecture 7. Legendre’s necessary condition
• Lecture 8. Jacobi’s necessary condition
• Lecture 9. Weak versus strong variations
• Lecture 10. Weierstrass’s necessary condition
• Lecture 11. The transversality conditions
• Lecture 12. Hilbert’s invariant integral
• Lecture 13. The fundamental sufficient condition
• Lecture 14. Jacobi’s condition revisited
• Lecture 15. Isoperimetrical problems
• Lecture 16. Optimal control problems
• Lecture 17. Necessary conditions for optimality
• Lecture 18. Time-optimal control
• Lecture 19. A singular control problem
• Lecture 20. A biological control problem
• Lecture 21. Optimal control to a general target
• Lecture 22. Navigational control problems
• Lecture 23. State variable restrictions
• Lecture 24. Optimal harvesting
• Afterword
• Solutions or hints for selected exercises

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