Yuanyuan Shi, yyshi@eng.ucsd.edu
Jie Feng, jif005@ucsd.edu
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
Lecture 1: Introduction and Course Logistics [Lecture 1]
Lecture 2: Linear Algebra and ODEs review [Lecture 2]
Lecture 3: System Modeling [Lecture 3]
Lecture 4: Dynamic Behavior, Equilibrium, and Linearization [Lecture 4]
Lecture 5: Stability of LTI Systems [Lecture 5]
Lecture 6: Controllability/Reachability of LTI Systems [Lecture 6]
Lecture 7: More Controllability Tests [Lecture 7]
Lecture 8: State Feedback Control and Eigenvalue Placement [Lecture 8]
Lecture 9: Linear Quadratic Regulator (LQR) [Lecture 9]
Lecture 10: Lyapunov Stability Analysis [Lecture 10]
Lecture 11: Midterm Review [Lecture 11]
Lecture 12: Observability of LTI Systems [Lecture 12]
Lecture 13: State Estimation and Output Feedback [Lecture 13]
Lecture 14: Kalman Filter [Lecture 14]
Lecture 15: More Observability Tests [Lecture 15]
Lecture 16: LQG and Trajectory Tracking [Lecture 16]
Lecture 17: Stabilizability and Detectability [Lecture 17]
Lecture 18: Reinforcement Learning I [Lecture 18]
Lecture 19: Reinforcement Learning II [Lecture 19]
Lecture 20: Final Exam Review [Lecture 20]
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.Â