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

MAE 507: Modern Optimal Control

Textooks:

A Course in Robust Control Theory: A Convex Approach

G. E. Dullerud and F. PaganiniTaught in Spring, 2009; Fall, 2010; Fall, 2011

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.

Lectures: Modern Optimal Control

[Lecture 1] - Modern Control Systems

[Lecture 2] - Mathematical Preliminaries

[Lecture 3] - Normed Spaces, Matrix Properties

[Lecture 4] - Back to Matrices

[Lecture 5] - Controllability and Observability

[Lecture 6] - Controllability and Observability

[Lecture 7] - Canonical Forms and Stabilizability

[Lecture 8] - Eigenvalue Assignment

[Lecture 9] - Observability

[Lecture 10] - Linear Systems Theory

[Lecture 11] - Linear Operators

[Lecture 12] - Small Gain Theorem

[Lecture 13] - The joy of Hilbert Space

[Lecture 14] - Operators on Signal Space

[Lecture 15] - Linear Causal Time-Invariant Operators

[Lecture 16] - Summary of Linear Analysis

[Lecture 17] - Grammians

[Lecture 18] - The Optimal Control Framework

[Lecture 19] - Stabilization via LMIs

[Lecture 20] - Optimal Full-State Feedback Control

[Lecture 21] - Optimal Output Feedback Control

[Lecture 22] - H2, LQR and LQG

[Lecture 23] - Introduction to Robust Control