Materials

This course is presented as a series of interactive lectures that combine basic Python code examples with theoretical discussion. Simply open the link in your browser to view the slides; we are also working on making the slides available in a code-free HTML format. If you want to follow along with the lectures interactively (with the ability to run the code), you’ll need to install Python’s rise and download the jupyter-notebook version of the slides.

Format of Slides and Notes

The majority of the slides also have accompanying notes that can be viewed online or downloaded as a pdf (though it should be noted that the pdf is automatically generated and may contain some errors). In addition, we have made the jupyter notebooks available on google colab, so you can try out the interactive components of the course right in your browser without the need for any additional installations.

Part 1: Introduction to Modeling, System Analysis and Control

Lecture 1: Modeling and State Space

Description: The introduction to modeling and state space representation, the mechanical systems, several examples of state space models

Lecture 2: Basics of Analysis and Control

Description: The basics of analysis and control of linear and nonlinear systems, stability, pole placement, linearization and lyapunov analysis

Supplementary material:

1. Linearization based control of cart pole system

Lecture 3: Lyapunov Stability Theory

Description: Introduction to the stability analysis over nonlinear systems, Lyapunov direct method with applications to regional analysis (basin of attraction and invariant sets)

Part 2: Optimization in Control

Lecture 4: Optimal Control, LQR

Description: The notion of Optimal Control. Bellman optimality, Linear case: LQR controller, Riccatti equations, relation between value and Lyapunov functions

Supplementary material:

1. Linearization based LQR control of cart pole system
2. Example of LQR design for satellite maneuver

Lecture 5: Model Predictive Control

Description: Finite horizon LQR as leas squares. Incorporating constraints in to optimal linear control, quadratic programming, receding horizon and online planning as controller.

Supplementary material:

1. CVXPY based linear MPC over linearized cart pole

Lecture 6: Trajectory Optimization

Description: Trajectory optimization over nonlinear systems, finite horizon optimal control, nonlinear optimization. Differential flatness.

Supplementary material:

1. Swing-up for cart pole with trapezoidal collocation
2. Soft landing trajectory for 1-DoF simplified model of Apollo 11, adding time to decision variables

Lecture 7: Linear Matrix Inequality in Control

Description: Semi-definite programming, Lyapunov based control via linear matrix inequalities

The content of this lecture is in progress

Lecture 8: Control Lyapunov and Barrier Functions

Description: The notion of Control Lyapunov Functions, Sontag Formula, Control as QP, Safety, Barrier Method and CBF

The content of this lecture is in progress

Part 3: System Identification, Model Reduction and Data Driven Control

Lecture 9: Basics of System Identification and Parameter Estimation

Description: The notion of System Identification

The content of this lecture is in progress

Lecture 10: System Identification Methods

Description: ERA, SINDY, ETC

The content of this lecture is in progress

Lecture 11: Data Driven Linearization

Description: Koopman, Dual Faceted Linearization

The content of this lecture is in progress

The lecture material is continually revised and updated, and over time, additional information will be made available on this site that was not covered in class (primarily due to time constraints).