# ECE171B Linear Control SysteM Theory

# 2022 Fall

### Instructor

Yuanyuan Shi, yyshi@eng.ucsd.edu

### Teaching Assistant

Jie Feng, jif005@ucsd.edu

### Course Syllabus

This course provides an introduction to systems and control in physical, biological, engineering, information, financial, and social sciences, etc. Key themes include linear system modeling, linear system stability, eigenvalue placement, state feedback controller design, LQR, observability, output feedback controller, and an introduction to reinforcement learning (and its connection to control theory), etc. It includes both the practical and theoretical aspects of the topic.

Topics Include

Review of Linear Algebra and ODE

System Modeling

Linearization and Linear Time-Invariant Systems

Linear System Stability

Lyapunov Stability and Lyapunov Equation

Reachability

Eigenvalue Placement

State Feedback Control

Optimal Control: Linear Quadratic Regulator

Observability and State Estimation

Output Feedback Control

Introduction to Reinforcement Learning and Connection to Control

### Lectures

Lecture 1: Introduction and Course Logistics [Lecture 1]

Lecture 2: Linear Algebra and ODEs review [Lecture 2]

Lecture 3: System Modeling I [Lecture 3]

Lecture 4: System Modeling II [Lecture 4]

Lecture 5: Dynamic Behavior [Lecture 5]

Lecture 6: Linearization [Lecture 6]

Lecture 7: Matrix Exponential [Lecture 7]

Lecture 8: Stability of Linear Systems [Lecture 8]

Lecture 9: Lyapunov Stability Analysis [Lecture 9]

Lecture 10: Reachability [Lecture 10]

Lecture 11: Eigenvalue Placement [Lecture 11]

Lecture 12: Linear Quadratic Regulator (LQR) [Lecture 12]

Lecture 13: Midterm Review

Lecture 14: Observability and State Estimation [Lecture 14]

Lecture 15: Output Feedback Control [Lecture 15]

Lecture 16: Kalman Filter [Lecture 16]

Lecture 17: Reinforcement Learning and Connection with Control [Lecture 17]

Lecture 18: Reinforcement Learning II [Lecture 18]

Lecture 18: Reinforcement Learning III [Lecture 19]

Lecture 20: Final Exam Review [Lecture Note]

### Course Textbook

Karl J. Astrom and Richard M. Murray, Feedback Systems: An Introduction for Scientists and Engineers (Second Edition), Princeton University Press. Available at: https://fbswiki.org/wiki/index.php/Feedback_Systems:_An_Introduction_for_Scientists_and_Engineers

Acknowledgment: much of the class material is based on Prof. Na Li at Harvard University and her class on ES 155: Systems and Control; and Prof. Richard Murray at Caltech and his course on CDS 101/110 Introduction to Control Systems.