COURSE DESCRIPTION
This course investigates how to model, analyze, and control dynamical systems!
COURSE WEBSITE
This page: /ece6550.html
WORKLOAD
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.
PROGRAMMING
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.
READING
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.
TIME AND PLACE
The lectures will be held at 9:00-10:00 Mondays, Wednesdays, and Fridays in Klaus 2443.
PREREQUISITES
It is expected that students entering this class will have some basic
understanding of linear algebra, control theory, and differential equations.
HONOR CODE
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.
SCHEDULE
Date | Lecture subject | Reading/Homework |
Aug. 18 | Introduction and course outline | |
Aug. 20 | Beyond classic control? | |
LINEAR SYSTEMS | ||
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 |
STABILITY | ||
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 | |
CONTROLLABILITY AND OBSERVABILITY | ||
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 |
CONTROL DESIGN | ||
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 |