Lecture Notes: Introduction to Adaptive Control and Learning

Introduction

• Speaker's background in adaptive control
  • Over a decade of experience
  • PhD focused on adaptive control
  • Collaborated with various agencies (NSF, NASA, Air Force, DARPA)
  • Implemented adaptive control on systems like NASA Airstar

Importance of Adaptive Control

• All physical systems face disturbances and uncertainties:
  • Examples include:
    • Quadcopters: affected by wind and turbulence
    • Robotic arms: subject to friction
    • Systems linearized around equilibrium points: uncertainties arise when deviating
    • Unknown parameters or estimation errors
    • Actuator issues (e.g., icing)
    • Structural damages
• These disturbances negatively impact stability and performance, necessitating adaptive control.

Example: Mass-Spring-Damper System

• Components of the system:
  • Mass (m), spring constant (α), damper constant (β)
  • Position (P) and control signal (U)
• Modeling:
  • Utilize free body diagrams and Newton's second law (M*A = applied forces)
  • Represent system in state space:
    • Define states (X1, X2) for position and velocity
    • Formulate state-space equations incorporating unknown parameters*

Dealing with Uncertainties

• Two common control approaches:
  1. Robust Control:
     • Fixed parameters in algorithms.
     • Tuned for worst-case scenarios.
     • Requires knowledge of bounds on uncertainties.
  2. Adaptive Control:
     • Parameters change in real time.
     • Adapts to changes in the system.
     • Does not overly rely on model accuracy or bounds.
     • Performance can be unpredictable without proper learning structure.
• Adaptive control is often nonlinear, making it less understood compared to linear robust control.

Course Vision

• Aim for the best lecture series on adaptive control and learning.
• Coverage includes different types of uncertainties, designing learning algorithms, and more.

Recommended Resources

• Recommended Book:
  • "Adaptive Control" by Eugene Lavretsky and Kevin Wise
• Additional Reading:
  • Wiley Encyclopedia article on model reference adaptive control (2019)

Prerequisites for the Lecture Series

• Strong understanding of linear control systems and Lyapunov theory.
• Recommended to refresh knowledge via:
  • Previous videos on state space representation.
  • Stability concepts (Lyapunov stability, eigenvalues).
  • Control topics (state and output feedback, pole placement, optimal control).
  • Vector and matrix operations.

Conclusion

• Excited to begin the lecture series on adaptive control and learning.
• Encourages students to stay tuned for upcoming videos.