Short Course Description
Problem formulation in the continuous and discrete time. Bolza, Lagrange and Mayer problems. Relation with calculus of variations. Historical tour.
Static optimization: necessary and sufficient conditions for extremum, Lagrange multipliers.
Calculus of variations: the basic variational problem, the central Lemma, Euler-Lagrange condition, Legendre condition. Constrained variational problem: constraints in the form of differential equations, isoperimetric problem.
Pontryagin minimum principle: continuous-time. LQR problem and Riccati equations. The
tracking problem. Constrained input problems: minimum time, minimum fuel and minimum energy problems. Singular optimal control.
Dynamic programming: Bellman?s principle of optimality, dicsrete-time and continuous-time
problems. Hamilton-Jacobi-Bellman equation.
Necessary optimality conditions in the discrete-time: LQR problem and Riccati equations.
Introduction to differential games and H? control.
Full syllabus is to be published
