Optimal Control

Examples, basic properties of control systems, existence of a solution, continuity with respect to initial conditions and controls. Controllability of linear systems, non-linear controllability with Lie brackets. Lyapunov stability, retroaction laws. Optimal control problems, existence of optimal solution, optimality conditions, Pontryagin's Maximum Principle, Legendre-Clebsch conditions, second order conditions. Systems related to control, bang-bang solutions, bang-bang principle, singular arcs. Dynamic programming, Hamilton-Jacobi-Bellman equation. Optimal linear-quadratic control. Shooting method, straight methods. Applications.

Basic Information

45 hours
Functional Analysis: Fundamentals, Functional Analysis: Linear Operators, Measure, Integration and Probability


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  • R. Vinter. Optimal control. Modern Birkhäuser Classics. Birkhäuser Boston, Inc., Boston, MA, 2010. Paperback reprint of the 2000 edition


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  • J.-M. Coron. Control and nonlinearity. Number 136. American Mathematical Soc., 2007
  • L.C. Evans. An introduction to mathematical optimal control theory. Lecture Notes, University of California, Department of Mathematics, Berkeley, 2005