🚀 CMU16-745 Optimal Control 2023: Comprehensive Lecture Notes

👀 Course Overview

In this course, Prof. Zac offers an in-depth exploration into the realm of optimization-based control. The lecture notes provided here have been meticulously organized to ensure a structured and comprehensive understanding of the subject matter. Dive into the fascinating world of optimal control through the following topics:

Basics of Optimal Control

1. Introduction to Dynamics (Lecture 1)

   • Understanding the fundamental principles of dynamics.
   • How dynamics plays a crucial role in control systems.

2. Discretization (Lecture 2)

   • The importance of discretizing continuous systems.
   • Methods and techniques for effective discretization.

3. Optimization (Lectures 3-5)

   • Delving deep into the optimization techniques.
   • The role of optimization in control systems.

4. Deterministic Optimal Control (Lecture 6)

   • Introduction to deterministic approaches in optimal control.
   • Benefits and challenges of deterministic methods.

Basic Optimal Control Algorithms

Dive into the intricacies of control algorithms, ranging from time-invariant to time-varying systems, linear to nonlinear, and unconstrained to constrained systems.

1. No Constraints:

   • LQR for Time-Invariant Linear Systems (Lecture 7)
     • Exploring the Quadratic Programming (QP), shooting, and Riccati Recursion (RR) methods.
   • LQR for Time-Varying Linear Systems (Lecture 8)
     • Understanding the Dynamic Programming (DP) approach.

2. Constrained Systems:

   • MPC for Time-Varying Nonlinear Systems (Lectures 9-11)
     • Techniques like Quadratic Programming (QP), Second Order Cone Programming (SOCP), and non-linear optimizers.
   • DIRCOL for Time-Varying Nonlinear Systems (Lecture 12)
     • A deep dive into the Direct Collocation (DIRCOL) method.

Advanced Optimal Control

Venture into the advanced realms of optimal control with the following topics:

1. Adaptive Control (Lecture 17)

   • The evolving nature of adaptive control.
   • Real-world applications and challenges.

2. Stochastic Optimal Control and LQG/Kalman Filter (Lectures 18-19)

   • The probabilistic approach to optimal control.
   • Understanding the Linear Quadratic Gaussian (LQG) and the Kalman filter.

3. Robust Control (Lecture 20)

   • Ensuring stability and performance in the face of uncertainties.

4. Reinforcement Learning (Lecture 24)

   • Bridging the gap between control theory and machine learning.

Practical Control Systems

Delve into the practical aspects of control systems with the following topics:

1. 3D Rotation in Modelling and Optimization (Lectures 13-15)

   • Techniques and challenges in 3D rotational dynamics.

2. Hybrid Systems with Contact (Lecture 16)

   • Understanding systems that exhibit both continuous and discrete dynamics.

3. Convex Relaxation and landing rocket (Lecture 21)

   • Techniques to simplify complex optimization problems.

4. Legged Robots and QPs for Control (Lecture 22)

   • Control strategies for dynamic and complex systems like legged robots.

5. Autonomous Driving and Game Theory (Lecture 23)

   • Exploring the intersection of control, autonomy, and game theory.

💁‍♂️ Acknowledgments

A heartfelt thank you to Prof. Zackory Manchester for his invaluable disclosure of lecture videos, notes, and interactive notebooks.

🏷️ Disclaimer

While every effort has been made to ensure the accuracy of these notes, the author does not come from a traditional control background. As such, there may be inadvertent errors or misunderstandings. Readers are encouraged to raise any issues they find, and discussions are always welcome. Please remember that all content in this repository is strictly for educational purposes. Unauthorized use or distribution is prohibited.

🗳️ Resources

• Lecture Notebooks
• Official Lecture Notes
• Course Syllabus
• Video Lectures Playlist