ASE6029: Linear optimal control

Course Info.

Course descriptions

• The first graduate level course in systems and control. Covered topics include linear dynamical systems described in continuous time and discrete time domains, controllability and observability, linear quadratic optimal control and estimation problems, various techniques for solving linear quadratic regulators and Kalman filters.

Instructors

• Jong-Han Kim (Rm.507 @Aerospace campus)

Lectures

• Tue/Thr 14:30-15:45 (Rm.215 @aerospace campus)

Office hours

• JHK: Tue/Thr 16:00-17:00 (Rm.507), or by appointments.

Prerequisites

• Linear algebra and statistics

• Classical control and programming languages (Python or MATLAB).

Reference textbooks

• There are no required textbooks.

• Linear systems theory by Hespanha, Princeton university press.

• Linear controller design: Limits of performance by Boyd and Barratt, Prentice-Hall.

• EE263: Introduction to linear dynamical systems, a Stanford course by Boyd and Lall.

• EE363: Linear dynamical systems, a Stanford course by Boyd.

Grading policy

• Homework assignments (80%)

• Class participation (20%)

Course contents

1. Linear dynamical systems

2. Controllability and state transfer

3. Observability and state estimation

4. Linear quadratic regulators

5. Dynamic programming

6. Constrained optimization

7. Estimation

8. Kalman filter

9. Nonlinear filtering

10. Partially observed linear quadratic stochastic control

Computational exercises

1. Phase portrait

2. Eigenvectors and modes

3. Impulse response

4. Least norm control

5. Discrete LQR

6. Receding horizon control

7. Infinite horizon LQR

8. Optimal guidance solutions

9. Linear estimation

10. Covariance propagation

11. Kalman filter

Assignments

1. HW#1 (due 9/14)

2. HW#2 + Formation flight (due 9/29)

3. HW#3 (due 10/19)

4. HW#4 (due 11/2)

5. HW#5 (due 11/28)

Exams

1. To be assigned