E6602 Modern Control Theory

Department of Electrical Engineering, Columbia University

This webpage provides an overview of the E6602 Modern Control Theory class. E6602 is typically taught once per year. The information below is meant to provide a snapshot of the course structure and the material covered.

Overview

Course description

In this course, you will learn to recognize, model, formulate and solve optimal control problems that arise in a diverse range of applications including; circuits, mechanics, robotics, finance, etc. The primary object of interest will be linear time-invariant dynamical systems. We will begin with a primer of convex optimization and least squares problems. We will then cover state space models, system analysis (stability, controllability, observability), feedback control via linear matrix inequalities (H-infinity and H2 optimal control). Finally we will more advanced topics such as system identification (learning a dynamic model from data), uncertain systems, and distributed control.

Some sample classes and the schedule are shown below.

Week Topic Slides Additional notes
1 Intro & background Vector space notes
2 Least-squares
3 Linear systems
4 Stability of autonomous systems
5 Convex optimization LQR derivations
6 Controllability & state feedback
7 Minimum-norm control
8 Observability and observeres
9 BIBO stability
10 System performance & KYP lemma
11 Small gain theorem
12 H-infinity state feedback control
13 H-infinity output feedback control
14 Uncertain systems

Intended audience

This class is intended for students with an interest in the mathematical foundations of modern systems and control theory and those wishing to deploy optimal control algorithms to real applications. We particularly encourage students from non-engineering disciplines such as finance, biology, and physics.

Textbook

The course doesn't follow one specific book; all necessary material will be provided. However, we will draw heavily on material from:

  • A course in robust control theory: a convex approach
    Dullerud & Paganini
    Vol. 36. Springer Science & Business Media, 2013.

  • LMIs in control systems
    Duan & Yu
    CRC press, 2013.

An additional useful reference is

  • Linear matrix inequalities in system and control theory
    Boyd, El Ghaoui, Feron,& Balakrishnan
    SIAM, 1994.

Sample course projects

The projects below are a sample of past student projects:

Course organization

Prerequisites

  • Linear algebra: APMA E3101 linear algebra or comfortable with the material here.

  • Signals and systems: E3801 or equivalent.

  • Optimization: any optimization class (E4650 is ideal but not necessary, E6616 is being taught this semester).

In addition, familiarity with basic programming will be necessary to complete some homework questions. One of CVX (Matlab), CVXPY (Python), CVXR (R), or Convex.jl (Julia) will be used to write simple scripts. No prior knowledge of CVX is assumed, a recitation on this topic will be provided.

Students are required to use LaTeX to typeset their homework (undergraduates are encouraged to use LaTeX, but it is not a requirement). Templates and examples will be provided.

Grading

  • Homework 40%

  • Midterm exam 20%

  • Project 40%

Homework

There will be approximately 6 homework exercises set. All homeworks are due ten days after they are released and must be submitted via Gradescope. Homework submitted up to two days late will score a maximum of 50%, anything later will not be graded. When computing your overall grade for homework, we will drop your lowest scoring submission.

Apart from homework 1, students must typeset homework using LaTeX. A template will be provided. Students should read the style guide (written by Stephen Boyd for his EE364a class at Stanford) before submitting homework assignments.

Midterm

Closed-book midterm held during class time. Date tba.

Project

Students will develop their own system models, with the aim of simulating, analyzing, and designing feedback controllers. The project will consist of 3 components:

  • Proposal

  • Midterm progress report

  • Final report (conference style paper)

Details will be provided in class.