Educational Material:

"ATTENTION: Development of the educational material on this website was supported by the National Science Foundation under Grants No. 1100376, 1151018, 1301851, 1301660, 1538374, 1739990, 1931270, 1935453."

MAE 509: LMI Methods in Optimal and Robust Control

Textooks:
LMIs in Control Systems: Analysis, Design and Applications
G.-R. Duan and H.-H. Yu

Wikibook:
LMIs in Control
M. Peet et al.

Linear Matrix Inequalities in System and Control Theory
Boyd, El Ghaoui, Feron and Balakrishnan

A Course in Robust Control Theory: A Convex Approach
G. E. Dullerud and F. Paganini

Taught in Fall, 2016, 2017, 2019, 2020, 2021, 2022, 2023
Syllabus

Introduction: This class considers the basics of modern optimal control theory, with an emphasis on convex optimization and Linear Matrix Inequalities. We cover Mathematical Analysis, State-State Theory, Linear Systems Theory and H-infinity and H-2 optimal control using LMI formulations.

Required Software: SOSTOOLS 4.00 (Available via Matlab Toolbox Manager) and Sedumi or Mosek

 

Lectures: LMI Methods in Optimal and Robust Control

[Lecture 1] - Current Trends in Computation and Control
Video Link: [Part 1] [Part 2]

[Lecture 2] - Optimization
Video Link: [Part 1][Part 2]

[Lecture 3] - Relaxations, Duality, Cones, Positive Matrices, LMIs
Video Link: [Part 1]

[Lecture 4] - LMIs for State-Space Internal Stability
Video Link: [Part 1] [Part 2] [Part 3]

[Lecture 5] - LMIs for Controllability and Feedback Stabilization
Video Link: [Part 1] [Part 2] [Part 3] [Part 4]

[Lecture 6] - LMIs for Observability and Observer Design
Video Link: [Part 1] [Part 2] [Part 3]

[Lecture 7] - LMIs for the H2 and H-infinity Norms of Systems and Transfer Functions
Video Link: [Part 1] [Part 2] [Part 3] [Part 4]

[Lecture 8] - The Optimal Control Framework
Video Link: [Part 1] [Part 2]

[Lecture 9] - An LMI for H-infinity-Optimal Full-State Feedback Control
Video Link: [Part 1]

[Lecture 10] - An LMI for H-infinity-Optimal Output Feedback Control
Video Link: [Part 1] [Part 2] [Part 3]

[Lecture 11] - Relationship between H2, LQG and LGR and LMIs for state and output feedback H2 synthesis
Video Link: [Part 1] [Part 2] [Part 3]

[Lecture 12] - Modeling Uncertainty and Robustness
Video Link: [Part 1] [Part 2] [Part 3] [Part 4]

[Lecture 13] - LMIs for Optimal Control and Quadratic Stability with Affine Polytopic and Interval Uncertainty
Video Link: [Part 1] [Part 2]

[Lecture 14] - LMIs for Robust Control in the LFT Framework
Video Link: [Part 1] [Part 2] [Part 3]

[Lecture 15] - Nonlinear Systems and Lyapunov Functions
Video Link: [Part 1] [Part 2] [Part 3] [Part 4]

[Lecture 16] - Optimization of Polynomials and an LMI for Global Lyapunov Stability
Video Link: [Part 1] [Part 2] [Part 3]

[Lecture 17] - The PositivStellenSatz and an LMI for Local Stability
Video Link: [Part 1] [Part 2] [Part 3]

[Lecture 18] - SOS for Robust Stability and Control

[Lecture 19] - Hybrid Systems

[Lecture 20] - LMI/SOS Tools for the Study of Hybrid Systems