 2014 - 2015 | |||||||||||||||||||||||||||||
 |
 |
||||||||||||||||||||||||||||
| 0510-6301-01 | Optimal Control | ||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| FACULTY OF ENGINEERING | |||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||
University credit hours: 3.0
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 sucient conditions for extremum, Lagrange multipliers.
Calculus of variations: the basic variational problem, the central Lemma, Euler-Lagrange con-
dition, Legendre condition. Constrained variational problem: constraints in the form of di erential
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 di erential games and H∞ control.