# ME 562 - Robust Adaptive Control

## Course Information

Overview: 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 $$\mathcal{L}_1$$ adaptive control. Various examples will be discussed throughout the course to illustrate the results.

Team:

Instructor:

Office Hour: By appointment

Teaching Assistant:

Office Hour: Piazza or by appointment

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

Textbook: Hovakimyan, N., & Cao, C. (2010). $$\mathcal{L}_1$$​ Adaptive Control Theory: Guaranteed Robustness with Fast Adaptation. Society for Industrial and Applied Mathematics.

Lecture Notes: A pdf file can be downloaded here.

Lecture Videos: Each week some concepts will be presented through a collection of short video lectures.

Zoom Sessions: Each week Zoom Q&A sessions will be held for answering the questions from the course materials. Then, we have working sessions for discussion of homework problems and group projects, for which we will use breakout rooms.

Meetings Time (CDT) Location
Live Q&A and working sessions Mon & Wed 11 am Zoom: https://illinois.zoom.us/j/94479860234 (Password can be found here)

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.

Projects: 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 $$\mathcal{L}_1$$ adaptive control.

Grading: Project 1: Lyapunov stability analysis 30%; Project 2: MRAC design 30%; Project 3: $$\mathcal{L}_1$$​ adaptive control design 40%.

*If you have access issues to the course materials, please contact the teaching assistant.

## Schedule

Date Lectures Course Materials Notes
Week 1
(8/23 – 8/27)
Introduction
Mathematical Preliminaries
[slides01, video01] [slides02, video02] [slides03, video03] Group signup sheet
Week 2
(8/30 – 9/3)
Lyapunov Stability Theory for Autonomous Systems [slides04, video04] [slides05, video05] [slides06, video06] HW1
Week 3
(9/6 – 9/10)
No Zoom session on Mon. (Labor Day)
System Analysis based on Lyapunov's Direct Method
[slides07, video07] [slides08, video08] Project 1 info
Week 4
(9/13 – 9/17)
Lyapunov Stability Theory for Nonautonomous Systems
Boundedness and Ultimate Boundedness
[slides09, video09] [slides10, video10] Project 1 example
Week 5
(9/20- 9/24)
Model Reference Adaptive Control [slides11, video11] [slides12, video12] HW1 soln
Week 6
(9/27 – 10/1)
Presentation Week
(Project 1: Lyapunov stability analysis)
Week 7
(10/6 – 10/8)
Parameter Convergence
Direct MRAC for Nonlinear Systems with Matched Nonlinearities
[slides13, video13] [slides14, video14]
[Paper list]
HW2
Project 2 signup
Week 8
(10/11 – 10/15)
Robustness of MRAC: Parameter Drift
[slides15, video15] [slides16, video16] Project 2 example
Week 9
(10/18 – 10/22)
Adaptive Control in the Presence of Uniformly Bounded Residual Nonlinearity
Disturbance Rejection
[slides17, video17] [slides18, video18] HW2 soln
Week 10
(10/25 – 10/29)
Mathematical Preliminaries on $$\mathcal{L}$$-stability
$$\mathcal{L}$$-stability & Small-gain Theorem
[slides19, video19] [slides20, video20]
Week 11
(11/1 – 11/5)
Presentation Week
(Project 2: MRAC design)
Week 12
(11/8 – 11/12)
$$\mathcal{L}_1$$ Architecture for Systems with Known High-Frequency Gain & Transient and Steady-state Performance
Design Guidelines for Achieving Desired Specifications
[slides21, video21] [slides22, video22] Project 3 signup
Week 13
(11/15 – 11/19)
Performance Analysis and Stability Margins Analysis in Frequency Domain
Extension to Systems with Unknown Input Gain and Filter Design
[slides23, video23] [slides24, video24] Project 3 info
Week 14
(11/22 – 11/26)
Fall Break NASA Airstar Example: [slides25, video25]
Week 15
(11/29 – 12/3)
Output Feedback
Limiting Behavior of $$\mathcal{L}_1$$ Adaptive Controllers
[slides26, video26] [slides27, video27] Project 3 example
Week 16
(12/6 – 12/8)
Presentation Week
(Project 3: $$\mathcal{L}_1$$ adaptive control design)

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