Optimal Control (EE 60565)

University of Notre Dame


Description: Optimal control is concerned with control laws that extremalize a specified measure of a dynamical system's performance. This course is a rigorous introduction to the classical theory of optimal control. The topics covered in this course include optimization of static functions, the calculus of variations, Pontragin's principle, dynamic programming, linear quadratic optimal control, non-cooperative differential games with applications to control theory, and optimal stochastic control.
Topics:
  1. Maximum Principle and Compact Sets
  2. Kuhn-Tucker Conditions
  3. Euler-Lagrange Equations
  4. Optimal Control and Calculus of Variations
  5. Bang-Bang Principle
  6. Pontryagin's Maximum Principle
  7. Dynamic Programming Principle
  8. Hamilton-Jacobi Bellman equation
  9. Two person zero-sum differential games
  10. Finite Horizon H-infinity Control
  11. Stochastic HJB equation
Grading: 20 % homework, 40 % midterms, 40% final term paper.
Instructor: Michael Lemmon, Dept. of Electrical Engineering, University of Notre Dame (lemmon at nd dot edu)
Text:
  1. D. Kirk, Optimal Control Theory, Prentice-Hall, 1970.
  2. L.C. Evans An Introduction to Mathematical Optimal Control Theory: version 0.1, Unpublished lecture notes, U.C. Berkeley.

Additional References
  1. Bazarra, Sherali and Shetty, Nonlinear Programming: theory and algorithms, 2nd edition, John Wiley, 1993.
  2. T. Basar and G.J Olsder, Dynamic Noncooperative Game Theory, SIAM, 1999.
  3. D. Kirk, Optimal Control Theory, Prentice-Hall, 1970.
  4. L.C. Evans An Introduction to Mathematical Optimal Control Theory: version 0.1, Unpublished lecture notes, U.C. Berkeley.
  5. D. Wiberg, Notes for a couse in optimal control system, class lecture notes, UCLA, 1976.
  6. J. Macki and A. Strauss, Introduction to Optimal Control Theory, Springer, 1982.
  7. L. Hocking, Optimal Control: an introduction to the theory with applications, Claredon Press, OXford, 1991.
  8. P. Dorato, C. Abdallah, and V. Cerone, Linear Quadratic Control: an introduction, Prentice-Hall, 1995.
  9. E. Lee and L. Markus, Foundations of Optimal Control , Wiley, 1967.
  10. L. Young, Calculus of Variations and Optimal Control Theory, W.B. Saunders, 1969.
  11. W. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control, Springer-Verlag, 1975
  12. F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience Publication, 1983.
  13. M. Green and D.J.N Limebeer, Linear robust control , Prentice-Hall, 1995.
  14. M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhauser, 1997.
  15. E. Sontag, Mathematical Control Theory: deterministic fintie dimensional systems, Springer-Verlag, 1998.
  16. W. Rudin, Principles of Mathematical Analysis , McGraw-Hill, 3rd edition, 1976.
  17. D.P. Bertsekas, Dynamic Programming and Optimal Control , Athena Scientific, 2nd edition, 2000.