KOM 510E - Optimal Control Theory

Course Objectives

1. To provide basic concepts related to optimal control and its position in optimization
2. To teach the calculus of extrema and parameter optimization by the method of Lagrange multipliers
3. To teach the Optimality Principle and Dynamic Programming
4. To teach variational calculus and Pontragin’s minimum principle
5. To provide a solution approach for the Hamilton Jacobi-Bellman equation.
6. To provide the solution for Linear Optimal Control Problem (The Matrix Riccati Equation).

Course Description

Definition of optimization. Calculus of extrema and parameter optimization by the method of Lagrange multipliers. Performance measures. Optimality Principle and Dynamic Programming. Variational calculus and Pontragin’s minimum principle. Dynamic optimization in control systems for different terminal conditions. Hamilton Jacobi-Bellman equation. Linear Optimal Control Problem solution (The matrix Riccati equation). Optimization of discrete control systems. Numerical solution methods in optimal control problem.