MUH 453 - Introduction to Optimal Control Theory

Course Objectives

To introduce the optimal control systems, state the Pontryagin 's maximum principle, Lagrange principle and Bellman's dynamic programming method, apply the theory on popular mathematics and economy problems and design the solution algorithms.

Course Description

Historical development of the optimal control theory and actual problems. Introduction to the calculus of variation. Main differences between optimal control theory and calculus of variations. Pontryagin's maximum principle, its proof and examples. Formation of the optimal regulator with Riccati's equation for the linear systems with quadratic object functional. The synthesis problem and closed optimal loop. Lagrange principle, its proof and examples. Bellman's dynamical programming method. Controllable systems, their analytic characteristics and Kalman's theorem.