Feedback, Learning, and Adaptation

This course investigates the foundations of information, learning, and adaptation in the design and study of complex feedback systems. We will study notions of robustness, adaptivity, and optimization in feedback systems, and their associated principles, advantages, and disadvantages. We will compare the trade-offs between rich hierarchical modeling of complex systems and purely data-driven models for analysis and planning. In tandem, we will explore the roles of forecasting, estimation, predictive modeling, and retraining in automated decision making for these systems. The goal of the course will be to draw together disparate perspectives and evaluation metrics across control, machine learning, and decision theory to make sense of how we interact with complex, dynamic processes.

Introductory Blogs: (a) Induction and Feedback, (b) Feedback, Learning, and Adaptation - A Syllabus

References:

• (AR) Astrom, Karl J. “Model Uncertainty and Robust Control.” 2000.

• (AH) Astrom, Karl J. and Tore Hagglund. Advanced PID Control. Instrumentation, Systems, and Automation Society. 2006.

• (DFT) Doyle, John C., Bruce A. Francis, and Allen R. Tannenbaum. Feedback Control Theory. Macmillan Publishing Co., 1990.

• (PPA) Hardt, Moritz and Benjamin Recht Patterns, Predictions, and Actions. Foundations of Machine Learning. Princeton University Press, 2022.

• (Wil) Willems, J. C. “The Behavioral Approach to Open and Interconnected Systems.” IEEE Control Systems Magazine, vol. 27, no. 6, pp. 46-99, 2007.

• (Opt4DA) Wright, S. and Benjamin Recht. Optimization for Data Analysis. Cambridge University Press, 2022.

---

1. Lecture 1: Interconnection, robustness, and fragility

   1. Links and Loops

   2. Sweet spots for analysis

   3. Readings:

      1. DFT Chapters 2 and 3

      2. Wil pp 47-51

      3. Old Blog: The Soothing Warmth of Vacuum Tubes

2. Lecture 2: Fixed points and stability

   1. Matters of Life and Death

   2. All Downhill from Here

   3. Readings:

      1. Lecture notes on homeostasis

      2. S. Boyd. Basic Lyapunov Theory

      3. Bof et al. Lyapunov Theory for Discrete Time Systems

      4. L. Lessard. Lyapunov Functions