MAT 618 - Mathematical Optimal Control Theory II

Course Objectives

1 To introduce discrete time optimal control systems,
2 To introduce the maximum principle of Pontryagin,
3 To introduce Hamilton-Jacobi-Bellman equations
4 To introduce dynamic programming
5 To introduce constrained optimal control systems

Course Description

Historical development and current problems of the optimal control theory. Types of optimal control theory: Mayer, Lagrange, Bolza problems. Convex Analysis and extremum problems. Convex sets and functions. Convex programming. Set-valued functions. Optimization of discrete and differential inclusions. Pontryagin's maximum principle, proof and examples. Dynamic programming method of Bellman. Controllable systems, analytical characteristics and Kalman criterion. Infimal convolution. Duality problems.