Lectures for ECE1659H: Robust and Optimal Control (Winter 2022)

Lectures will be delivered synchronously online until February 6th, 2022. Recordings will be made available here. The Zoom link for lectures is here. The password will be made available on Piazza. There will be no lecture during Winter Study Week. Please see here for the most up to date scheduling information for in-person lectures, beginning on February 7th, 2022.

Lecture 1: Introduction, Vector Spaces, and Operators

• Recorded Lecture (link)

• Coverage: course contents, motivating examples, historical context for robust control, vector spaces, bounded operators, induced norms

• Suggested Reading: Dullerud & Paganini Chap. 0, 1.1

Lecture 2: Linear Operators, Mathematical Optimization, and Intro to LMIs

• Recorded Lecture (link)

• Coverage: SVD, optimization problems, convexity, affine mappings, PSD matrices and properties, LMIs

• Suggested Reading: Dullerud & Paganini Chap. 1.2, 1.3, 1.4, 3.1, 3.2. Boyd et al. Chap. 1, 2, 3. Scherer & Weiland Chap. 1.

Lecture 3: More LMIs, SDP Duality, Lyapunov Stability and Inequalities

• Video Lecture (link)

• Coverage: semidefinite programming duality, strong alternatives, Exponential stability, Lyapunov theory, Lyapunov LMI

• Suggested Reading: Scherer & Weiland Chap. 2, Dullerud & Paganini Chap. 4.1, 5.1, 5.2, Boyd et al. Chap. 5

Lecture 4: State Feedback via LMIs, Dissipative Dynamical Systems

• Video Lecture (link)

• Coverage: state-feedback design, stabilizability and strong alternatives, dissipativity with quadratic supply rates, non-strict dissipativity theorem for LTI systems

• Suggested Reading: Boyd et al. Chap. 6, Scherer & Weiland Chap. 2, Van Der Schaft Chap. 3

Lecture 5: Strictly Dissipative Systems, The KYP Lemma, Signals and Systems

• Video Lecture (link)

• Note: First half of lecture was not recorded due to tech. issue

• Coverage: The KYP lemma, strict dissipativity, interconnections of dissipative systems, L2 and extended L2 spaces, input-output stability notions

• Suggested Reading: Scherer & Weiland Chap. 2, Van Der Schaft Chap. 1, 2, 3

Lecture 6: Signals and Systems for Stability and Performance Analysis

• Video Lecture (link)

• Coverage: systems as signal-space operators, L2/H-Infinity performance, H2 performance

• Suggested Reading: Dullerud & Paganini Chap. 6.1, 9.1, Scherer & Weiland Chap. 3

Lecture 7: The H2 and H-Infinity State-Feedback and Output Feedback Control Problems

• Video Lecture (link)

• Coverage: LMI Solutions of suboptimal state feedback and output feedback problems

• Suggested Reading: Dullerud & Paganini Chap. 6.4, Boyd et al. Chap. 7. Dullerud & Paganini Chap. 7, Scherer & Weiland Chap. 4

Lecture 8: Stability and Performance of Uncertain Systems I

• Video Lecture (link)

• Coverage: robustness, LFR uncertainty model, examples, invertibility of matrix families

• Suggested Reading: Dullerud & Paganini Chap. 8, Scherer & Weiland Chap. 6

Lecture 9: Stability and Performance of Uncertain Systems II

• Video Lecture (link)

• Coverage: quadratic constraints, robust stability theorem, robust L2 and H2 performance

• Suggested Reading: Scherer & Weiland Chap. 7, El Ghaoui et. al. Chap. 6,7,10, Desoer & Vidyasagar Chap. 3, 6

Lecture 10: Introduction to Integral Quadratic Constraints

• Video Lecture (link)

• Coverage: IQCs in the frequency and time-domain, the soft IQC theorem

• Suggested Reading: Boyd et al. Chap. 8, Scherer & Weiland Chap. 7, Megretski/Rantzer ’97 TAC paper.