Optimal and robust control of PDEs

Didier GEORGES ( ).

Class schedule

Lesson Topic
1
Open-loop optimal control of PDE
Adjoint-based method for some particular PDEs: a parabolic and a hyperbolic PDE case studies; a short introduction to numerical methods for the solution of open-loop infinite-dimensional optimal control problems.
2
Optimal control of PDE with state-feedback
The Linear Quadratic Regulator; solution via the operator Riccati equation; two case studies.
3
Robust control of PDE with state-feedback
A game-theoretic approach: the Hinfinity optimal regulator; solution via the associated operator Riccati equation; one case study.

Class textbooks

  • R. F. Curtain and H. Zwart, "An Introduction to Infinite-Dimensional Linear Systems Theory", vol. 21 of Texts in Applied Mathematics, Springer-Verlag, New York, 1995.
  • E. Casas, "Optimal Control of PDEs", website .
  • A. Bensoussan and P. Bernhard, "On the standard problem of Hinfinity-optimal control problems for infinite-dimensional systems", Identification and control in systems governed by PDEs, pp. 117-140, SIAM, Philadephia (PA), 1993.
  • R. Curtain, A.M. Peters and B. Van Keulen, "Hinfinity-control with state-feedback: the infinite-dimensional case", Journal of Math. Syst. Estim. Control, vol. 3, nb. 1, pp. 1-39, 1993.

Grading Policy

Homeworks: 20 %

Final Exam: 80 %

Handouts

Restricted access area