Introduction to Calculus of Variations: Necessary and sufficient conditions for extrema. Euler-Lagrange equations. Extrema with constraints, Lagrange multipliers. Optimal Control: Control systems, Attainable sets, Topological properties, Controllability. The minimum time problem in the linear case, Extremal control, Maximum Principle. Minimization of quadratic cost in the linear case without input set constraints, Riccati equation. Nonlinear systems: Topological properties of attainable sets, extremal control, the general Maximum Principle (Pontryagin s Maximum Principle), Necessary conditions in optimal control problems with and without control constraints. Sufficient conditions and existence theorems. The Hamilton-Jacobi-Bellman equation. Applications.
- Teacher: Ιάσων Καραφύλλης
- Teacher: Ιωάννης Τσινιάς
ECTS : 5
Language : el