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This course provides a rapid overview of optimal control (controllability, observability, LQR, Kalman filter, etc.). It is not meant to be an exhaustive treatment, but instead provides a high-level overview of some of the main approaches, applied to simple examples in Matlab.
These lectures follow Chapter 8 from: "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz
Control Bootcamp: Overview.
Linear Systems [Control Bootcamp].
Stability and Eigenvalues [Control Bootcamp].
Linearizing Around a Fixed Point [Control Bootcamp].
Controllability [Control Bootcamp].
Controllability, Reachability, and Eigenvalue Placement [Control Bootcamp].
Controllability and the Discrete-Time Impulse Response [Control Bootcamp].
Degrees of Controllability and Gramians [Control Bootcamp].
Controllability and the PBH Test [Control Bootcamp].
Cayley-Hamilton Theorem [Control Bootcamp].
Reachability and Controllability with Cayley-Hamilton [Control Bootcamp].
Inverted Pendulum on a Cart [Control Bootcamp].
Pole Placement for the Inverted Pendulum on a Cart [Control Bootcamp].
Linear Quadratic Regulator (LQR) Control for the Inverted Pendulum on a Cart [Control Bootcamp].
Motivation for Full-State Estimation [Control Bootcamp].
Control Bootcamp: Observability.
Control Bootcamp: Full-State Estimation.
The Kalman Filter [Control Bootcamp].
Control Bootcamp: Observability Example in Matlab.
Control Bootcamp: Observability Example in Matlab (Part 2).
Control Bootcamp: Kalman Filter Example in Matlab.
Control Bootcamp: Linear Quadratic Gaussian (LQG).
Control Bootcamp: LQG Example in Matlab.
Control Bootcamp: Introduction to Robust Control.
Control Bootcamp: Three Equivalent Representations of Linear Systems.
Control Bootcamp: Example Frequency Response (Bode Plot) for Spring-Mass-Damper.
Control Bootcamp: Laplace Transforms and the Transfer Function.
Control Bootcamp: Benefits of Feedback on Cruise Control Example.
Control Bootcamp: Benefits of Feedback on Cruise Control Example (Part 2).
Control Bootcamp: Cruise Control Example with Proportional-Integral (PI) control.
Control Bootcamp: Sensitivity and Complementary Sensitivity.
Control Bootcamp: Sensitivity and Complementary Sensitivity (Part 2).
Control Bootcamp: Loop shaping.
Control Bootcamp: Loop Shaping Example for Cruise Control.
Control Bootcamp: Sensitivity and Robustness.
Control Bootcamp: Limitations on Robustness.
Control Bootcamp: Cautionary Tale About Inverting the Plant Dynamics.
Control systems with non-minimum phase dynamics.
Control Theory and COVID-19.
Control Theory and COVID-19: Sensors.
Control Theory and COVID-19: Summary.
Control Theory and COVID-19: Models.
Control Theory and COVID-19: Control Design.
Reinforcement Learning: Machine Learning Meets Control Theory.
Deep Reinforcement Learning: Neural Networks for Learning Control Laws.
Model Predictive Control.
Deep Reinforcement Learning for Fluid Dynamics and Control.
Steve Brunton
5.0 rating, based on 2 Class Central reviews
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