# 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 Note]

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

Lecture 3: System Modeling I [Lecture Note]

Lecture 4: System Modeling II [Lecture Note]

Lecture 5: Dynamic Behavior [Lecture Note]

Lecture 6: Linearization [Lecture Note]

Lecture 7: Matrix Exponential [Lecture Note]

Lecture 8: Stability of Linear Systems [Lecture Note]

Lecture 9: Lyapunov Stability Analysis [Lecture Note]

Lecture 10: Reachability [Lecture Note]

Lecture 11: Eigenvalue Placement [Lecture Note]

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

Lecture 13: Midterm Review

Lecture 14: Observability and State Estimation [Lecture Note]

Lecture 15: Output Feedback Control [Lecture Note]

Lecture 16: Kalman Filter [Lecture Note]

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

Lecture 18: Reinforcement Learning II [Lecture Note]

Lecture 18: Reinforcement Learning III [Lecture Note]

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.