# ECE171B Linear Control SysteM Theory

# 2021 Fall

### Instructor

Yuanyuan Shi, yyshi@eng.ucsd.edu

### Teaching Assistant

Alakh Desai, ahdesai@eng.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 and time-domain state-space analysis, stability, observability, state/output feedback controller, reference tracking, 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

Reachability

Eigenvalue Placement

State Feedback Control

Observability and State Estimation

Output Feedback Control

Optimal Control: Linear Quadratic Regulator

(Stretch) Reinforcement Learning

### Lectures

Lecture 1: Introduction and Course Logistics [Lecture Note]

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

Lecture 3: Linear Algebra and ODEs review II [Lecture Note]

Lecture 4: System Modeling I [Lecture Note]

Lecture 5: System Modeling II [Lecture Note]

Lecture 6: Dynamic Behavior [Lecture Note]

Lecture 7: Linearization [Lecture Note]

Lecture 8: Linear Time-Invariant Systems and Stability [Lecture Note]

Lecture 9: Midterm Review

Lecture 10: Matrix Exponential [Lecture Note]

Lecture 11: Reachability [Lecture Note]

Lecture 12: Eigenvalue Placement [Lecture Note]

Lecture 13: Linear Quadratic Regulator (LQR) [Lecture Note]

Lecture 14: Observability and State Estimation [Lecture Note]

Lecture 15: Output Feedback Control [Lecture Note]

Lecture 16: Kalman Filter and LQG [Lecture Note]

Lecture 17: Reinforcement Learning I [Lecture Note]

Lecture 18: Reinforcement Learning II [Lecture Note]

Lecture 19: PID Control [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

Acknowledgement: 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.