ELL 801: Nonlinear Control

Nonlinear Control course covers the analysis and design of nonlinear control systems. By the end of the course, it is expected that the students would have learned about various tools for the control of nonlinear systems and played around with a variety of interesting nonlinear examples.

Notes

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

• Feedback linearization: SISO systems (Chapter 13, Kh; Chapters 5-6, Ni; Chapter 4, Is)
  

• Observers with linear error dynamics (Chapter 4, Is; Chapter 14, Kh)
  

• Feedback linearization: MIMO systems (Chapters 5,7 Is)
  

• Nonlinear controllability and observability (Chapter 3, Ni)
  

• Stabilization via nonlinear feedback (Chapter 5, So)
  

• Safety-critical control (Am, Hs)
  

Homeworks

• Homework#1 (due January 19, 2024)

• Homework#2 (due January 30, 2024)

• Homework#3 (due February 2, 2024)

• Homework#4 (due February 25, 2024)

• Homework#5 (due March 22, 2024)

• Homework#6 (due April 05, 2024)

• Homework#7 (due April 21, 2024)

Prerequisties

• Basic knowledge of state space models, differential equations, and linear algebra.
  

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

Grading Policy

• Homeworks: 30%
  

• Mid-term: 30%
  

• Major: 40%

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.
  

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

• (Am) A. D. Ames, J. W. Grizzle and P. Tabuada. Control barrier function based quadratic programs with application to adaptive cruise control. In 53rd 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, In American Control Conference, 2015.
  

Useful Software

• pplane

Class Schedule

• Mondays, Tuesdays, and Fridays: 12-12.50pm, II LT3.

Exam Schedule

• Mid-term: LH 512, 6-8pm, 27 February, 2024.
  

• Major: LH 527, 1-3pm, 3 May, 2024.