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
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.

Software: A Modified version of SOSTOOLS for use in combination with code listed in Lecture Notes. This should be used to replace SOSTOOLS and the folder SOSMOD should be added to the Matlab Path.

[SOSMOD_vMAE598.zip] - Compatible with Matlab 2015b and earlier. Some error messages in Matlab 2016b)

 

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