# AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution

# 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

### Table of Contents

**Front/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