ECE6550 - Fall 2014
Linear Systems and Control

Magnus Egerstedt

(404) 894-3484  
TSRB 432     

Office hours: Wednesdays 1-3 or by appointment

Teaching Assistant: Thiagarajan Ramachandran

This course investigates how to model, analyze, and control dynamical systems!


This page: /ece6550.html

Your responsibilities in this class will fall into two main categories:
1. The homework sets (one problem set roughly every third week) = 35%. The credit will be divided between programming assignments and theoretical exercises.
2. The midterm and final exams = 25% + 40% = 65% They will cover all the material presented in the class. They will be closed-book, closed-note, closed-calculator exams.

The objective with the programming assignments is to see how to bridge the gap between what's done in class and how to actually apply it. (The actual programming involved will be very minor.) The assignments will be Matlab-based.

The textbook is by Joao Hespanha. It is called Linear Systems Theory, Princeton University Press, 2009, and it will be supplemented by a few handouts from other sources.

The lectures will be held at 9:00-10:00 Mondays, Wednesdays, and Fridays in Klaus 2443.

It is expected that students entering this class will have some basic understanding of linear algebra, control theory, and differential equations.

Although you are encouraged to work together to learn the course material, the exams and homework are expected to be completed individually. All conduct in this course will be governed by the Georgia Tech honor code.


Date Lecture subject Reading/Homework

Aug. 18 Introduction and course outline
Aug. 20 Beyond classic control?

Aug. 22 State-space systems ch.1
Aug. 25 Realization theory ch.4.3
Aug. 27 Examples
Aug. 29 Dynamical systems ch.3
Sept. 1 Labor Day - NO CLASS
Sept. 3 Linear systems ch.3
Sept. 5 Some linear algebra ch.3, HW1 (state-space systems)
Sept. 8 The state transition matrix ch.5
Sept. 10 Matrix exponentials ch.6
Sept. 12 Cayley-Hamilton theorem ch.6, ch.7

Sept. 15 Preliminaries ch.8
Sept. 17 Eigenvalue tests ch.8
Sept. 19 Discrete-time systems ch.8, HW2 (linear systems)
Sept. 22 Lyapunov's direct method ch.8
Sept. 24 Lyapunov functions
Sept. 26 Review
Sept. 29 MIDTERM

Oct. 1 Vector spaces ch.11
Oct. 3 The reachability Gramian ch.11
Oct. 6 Controllability ch.11, ch.12
Oct. 8 The rank test ch.11
Oct. 10 Examples HW3 (stability)
Oct. 13 Fall Recess - NO CLASS
Oct. 15 Observability ch.15
Oct. 17 Duality ch.15
Oct. 20 Kalman decomposition ch.16
Oct. 22 Minimality ch.16, ch.17

Oct. 24 Feedback
Oct. 27 Pole placement ch.14.6, HW4 (controllability)
Oct. 29 Design choices
Oct. 31 Examples
Nov. 3 Output feedback ch.16
Nov. 5 Observers ch.16
Nov. 7 The separation principle ch.16
Nov. 10 Examples
Nov. 12 Introduction to optimal control ch.10, ch.20
Nov. 14 The Riccati equation ch.10, ch.20, HW5 (control design)
Nov. 17 Linear-quadratic regulators ch.20
Nov. 19 Finite and infinite horizons
Nov. 21 Model-predictive control
Nov. 24 Optimal estimation ch.23
Nov. 26 Kalman filter ch.23
Nov. 28 Thanksgiving - NO CLASS
Dec. 1 Beyond linear?
Dec. 3 At the research frontier
Dec. 5 Review
Dec. 10 FINAL EXAM: 8:00-10:50