ME 562: Robust Adaptive Control (Online)

Fall 2020

Course Information

Any of ME 460ECE 486, ECE 515, ECE 528and some elementary knowledge of differential equations.


Many dynamic systems to be controlled have both parametric and dynamic uncertainties. For instance, robot manipulators may carry large objects with unknown inertial parameters. Power systems may be subjected to large variations in loading conditions. Fire-fighting aircraft may experience considerable mass changes as they load and unload large quantities of water. Adaptive control theory is motivated by similar examples and offers solutions for controlling systems in the presence of uncertainties. This course presents a rigorous mathematical foundation for the synthesis and analysis of robust adaptive control systems. It covers fundamentals of Lyapunov stability theory and robust control, presents methods of direct and indirect model reference adaptive control, and places the focus on L1 adaptive control. Various examples will be discussed throughout the course to illustrate the results.

Topics Covered

Analysis Tools

Lyapunov’s stability theory
Autonomous systems
Non-autonomous systems
Boundedness analysis

Model Reference Adaptive Control (MRAC)

Direct and indirect adaptive control as inverse Lyapunov design
Robustness of adaptive systems to disturbance and measurement noise
Parameter convergence: persistent excitation
Parameter projection, e-modification, sigma-modification
Overview of adaptive output feedback control theory

L1 Adaptive Control: Transient Performance and Robustness

Norms and gains for signals and systems
Small-gain theorem
Achievable performance: Reference system and guaranteed performance bounds
Design system and decoupled performance bounds
State feedback architecture
Output feedback architecture
*To access course materials and assignments, you will need to use your @illinois email to access the course materials.

Lecture Videos

Each week some concepts will be presented through a collection of short video lectures. You may stream these videos for playback within the browser, but you may not download and distribute the videos.


Each week will have assigned readings from the lecture notes or textbook listed in the course information. These readings will provide details about all of the concepts for the week, as well as detailed proofs and examples.

Zoom Q&A sessions

Each week Zoom Q&A sessions will be held for answering the questions from the course materials. The Zoom link is posted in the Schedule on the course website.

Practice Homework Assignments

Two to three practice homework assignments and their solutions will be given as we cover the corresponding materials. Homework assignments are not going to be graded, but they are meant to be learning experiences in this course.


The grading will be based on three group projects (2-3 students per group). The groups will develop their own project proposals. It is desired to consider a nonlinear system and analyze its stability upon the first section of the course material on the Lyapunov stability theory. Midterm project progress will analyze the design of MRAC controllers for your chosen systems. The final presentation will be focused on the design of L1 adaptive control.

L1 Adaptive Control Theory: Guaranteed Robustness with Fast Adaptation

Naira Hovakimyan and Chengyu Cao
Series: Advances in Design and Control
ISBN: 978-0-898717-04-4
SIAM, Philadelphia, PA, 2010
Naira Hovakimyan
Wenbin Wan
Teaching Assistant

The grading will be based on three group projects:

Project 1: Lyapunov stability analysis 30%
Project 2: MRAC design 30%
Project 3: L1 adaptive control design 40%


Meetings Time Location
Live Q&A sessions MW 11 am Zoom:
Piazza Q&A platform Piazza:
* If you have access issues to the course materials, please email the teaching assistant.
Date Details Lecture Videos Readings Notes
Week 1
(8/24 - 8/28)
Mathematical Preliminaries
Lecture videos
01 - 03
Lecture notes
Group signup sheet available
Week 2
(8/31 - 9/4)
Lyapunov Stability Theory for Autonomous Systems Lecture videos
04 - 06
Lecture notes
Week 3
(9/7 - 9/11)
System Analysis based on Lyapunov's Direct Method
Lyapunov Stability Theory for Nonautonomous Systems
Lecture videos
07 - 08
Lecture notes
Week 4
(9/14 - 9/18)
Lyapunov Stability Theory for Nonautonomous Systems
Boundedness and Ultimate Boundedness
Lecture Videos
09 - 10
Lecture notes
Piazza: HW1;
Guidelines for Project 1.
Week 5
(9/21 - 9/25)
Model Reference Adaptive Control Lecture Videos
11 - 12
Lecture notes
Piazza: Hw 1 soln.
Week 6
(9/28 - 10/2)
Presentation Week (Project 1: Lyapunov stability analysis)
Week 7
(10/5 - 10/9)
Parameter Convergence
Direct MRAC for Nonlinear Systems with Matched Nonlinearities
Lecture Videos
13, 14
Lecture notes
8, 11
Week 8
(10/12 - 10/16)
Robustness of MRAC: Parameter Drift
Projection Based Adaptation
Lecture Videos
15 - 16
Lecture notes
12 - 13
Piazza: HW2: MRAC example.
Week 9
(10/19 - 10/23)
Adaptive Control in the Presence of Uniformly Bounded Residual Nonlinearity
Disturbance Rejection
Mathematical Preliminaries on L-stability
Lecture Videos
17 - 19
Lecture notes
14, 15, 18.1
Piazza: MRAC codes.
Week 10
(10/26 - 10/30)
L-stability & Small-gain Theorem
L1 Architecture for Systems with Known High-Frequency Gain & Transient and Steady-state Performance
Lecture Videos
20 - 21
Lecture notes
18.2 - 18.6
Week 11
(11/2 - 11/6)
Presentation Week (Project 2: MRAC design)
Week 12
(11/9 - 11/13)
Design Guidelines for Achieving Desired Specifications
Performance Analysis and Stability Margins Analysis in Frequency Domain
Lecture Videos
Lecture notes
18.7 - 18.11
Week 13
(11/16 - 11/20)
Extension to Systems with Unknown Input Gain and Filter Design
NASA Airstar
Lecture Videos
Lecture notes
18.12 - 18.17
Week 14
(11/23 - 11/27)
Fall Break
Week 15
(11/30 - 12/4)
Output Feedback
Lecture Videos
Lecture notes
Week 16
(12/7 - 12/9)
Presentation Week (Project 3: L1 adaptive control design)