ELL 8197: Advanced Topics in Systems and Control

This course covers the analysis and design of nonlinear control systems and, through the same stability and system-theoretic tools, the study of optimization algorithms as dynamical systems. By the end of the course, students are expected to have learned a range of tools for the control of nonlinear systems and to have seen how system-theoretic ideas extend to optimization.

Class Information

• Lecture schedule: Tuesdays and Wednesdays, 3.30-4.50pm, LH 623

List of Topics (Tentative)

• Introduction to feedback control, control via linearization, integral control (Chapter 12, Kh)
  

• Feedback linearization: SISO systems (Chapter 13, Kh)
  

• Feedback linearization: MIMO systems (Chapter 5, Is)
  

• Nonlinear controllability and observability (Chapter 3, Ni)
  

• Stabilization via nonlinear feedback (SoB; Chapter 5, SoA)
  

• Safety-critical control (Am; Hs)
  

• Gradient flows and convergence
  

• Constrained optimization dynamics
  

• Distributed optimization over networks
  

Homeworks

• Homework#1

• Homework#2

• Homework#3

Prerequisites

• Exposure to nonlinear dynamical systems.
  

• Familiarity with any simulation software (Matlab, Mathematica, Python, etc.).

Grading Policy

• Homeworks: 35%
  

• Mid-term: 30%
  

• Major: 35%

References

• (Kh) H. K. Khalil. Nonlinear Systems. Prentice Hall, 3rd edition, 2002.
  

• (Is) A. Isidori. Nonlinear Control Systems. Communications and Control Engineering Series. Springer, 3rd edition, 1995.
  

• (Ni) H. Nijmeijer and A. J. van der Schaft. Nonlinear Dynamical Control Systems. Springer, 1990.
  

• (SoA) E. D. Sontag. Mathematical Control Theory: Deterministic Finite Dimensional Systems. Number 6 in Texts in Applied Mathematics, 2nd edition, 1998.
  

• (SoB) E. D. Sontag. Stability and stabilization: Discontinuities and the effect of disturbances. Nonlinear Analysis, Differential Equations, and Control, 1999.
  

• (Am) A. D. Ames, J. W. Grizzle and P. Tabuada. Control barrier function based quadratic programs with application to adaptive cruise control. IEEE Conference on Decision and Control, 2014.
  

• (Hs) S.-C. Hsu, X. Xu and A. D. Ames. Control barrier function based quadratic programs with application to bipedal robotic walking. American Control Conference, 2015.
  

• (Ha) A. Hauswirth, Z. He, S. Bolognani, G. Hug, Florian Dörfler. Optimization algorithms as robust feedback controllers. Annual Reviews in Control, 2024.
  

Exam Schedule

• Mid-term: WS 101, 6-8pm, 13 September, 2026.