Course: EW418 Optimal Control and Estimation

3 Credits – 2 Recitation Hours – 2 Laboratory Hours


Course Description:

Analysis and design of control systems and estimators using optimal control theory.


Pre-requisites:

EW306 or EW306H

Course Coordinator:

Prof. Kiriakidis

Textbook:

None

Course Objectives:

  1. Use the Hamiltonian method for optimizing a performance index subject to constraints.

  2. Demonstrate the Euler-Lagrange condition to optimize functionals (brachisto).

  3. Apply Hamilton’s Principle to model trajectories for systems of objects.

  4. Use Jacobian matrix to linearize state equations about an operating trajectory.

  5. Demonstrate the necessary conditions to optimize functionals s.t.

nonlinear diff. constraints (min-time path problem).

linear diff. constraints (min-time “bang-bang”; min energy; fuel optimal).

  1. Apply optimization methods to address quadratic performance for linear models (LQR).

  2. Describe random environs in terms of white noise.

  3. Demonstrate the minimum variance averaging filter (Kalman-Bucy).

  4. Develop the sampled-data state equation (e.g., random walk).

  5. Demonstrate the prediction-correction Kalman Filter for state estimation.

Topics:

  1. The Optimal Control Problem

  2. The Optimal Estimation Problem in Gaussian Noise