EE222/ME237
Nonlinear Systems: Analysis, Stability, and Control

Course information: UCB On-Line Course Catalog and Schedule of Classes

• Professor Claire J. Tomlin, 721 SD Hall
• tomlin at eecs.berkeley.edu
• http://www.eecs.berkeley.edu/~tomlin
• Office hours: Tu 11-12, Wed 11-12

• Tyler Westenbroek, 337 Cory Hall
• westenbroekt at berkeley.edu
• Office hours: Mon 10-11, Thur 10-11 in Cory 337

• 1/16: The first lecture takes place on 1/21 in 105 North Gate.
• 1/23: There will be a discussion on Friday 1/24, 2:30-4 in Cory 540
• 2/7: The midterm will take place on Thursday March 5, in class
• 2/17: Starting with homework 4, we will now accept late submissions for homework on gradescope with 10% taken off each 24 hours after the submission.
• 3/4: As announced to the class email list today, the midterm test tomorrow will be a "take-home" test. The test will be provided to you online at 2:10pm tomorrow, and we require that you return it to us using bCourses, by 4pm tomorrow. This is meant to be a 1 hour and 20 minute test, and the extra time allows you to find a quiet place to work if you are coming from another class, download the test, and scan your solutions back for upload. We will send another email with instructions on downloading the test. The Honor Code is in effect: don't talk with others while taking the test, and use only your prepared crib sheet as supplemental material.
• 4/28: The final will be a take home exam, and you will have 24 hours to complete the exam. You are free to use your notes, textbooks, and lecture notes during the exam. The exam will be emailed to you at one of the following times, and you must upload it to Gradescope 24 hours after it was emailed to you. You may choose one of the following times (US Pacific time) to start the exam: Group 1: Thursday May 7 9am; Group 2: Thursday May 7 9pm; Group 3: Monday May 11 9am; Group 4: Monday May 11 9pm. Please let us know by May 6 at 5pm which group you prefer, by entering your name and preferred email to use for the exam, on the google sheet. If you do not enter your name, we will assume that you choose Group 4. The Honor Code is in effect: don't talk with others while taking the test, and do not pass information about the test to anyone until the entire exam period is over.

First graduate level course in nonlinear systems and control. Introduction to nonlinear phenomena: multiple equilibria, limit cycles, bifurcations, complex dynamical behavior. Planar dynamical systems, analysis using phase plane techniques. Describing functions. Input-output analysis and stability. Lyapunov stability theory. The Lure problem, Circle and Popov criterion. Control Lyapunov Functions. Feedback linearization, sliding mode control. The course will be punctuated by a rich set of examples, ranging from violin strings to jet engines, from heart beats to artificial neurons, and from population growth to nonlinear flight control.

• Introduction to Nonlinear Phenomena: Multiple Equilibria, Limit Cycles, Complex Dynamics, Bifurcations
• Second Order Nonlinear Systems: Phase Plane Techniques, Limit Cycles - Poincare-Bendixson Theory, Index Theory
• Input-output analysis and stability: Small Gain Theorem, Passivity, Describing Functions
• Lyapunov Stability Theory: Basic stability and instability theorems, LaSalle's theorem, Indirect method of Lyapunov, Control Lyapunov Functions
• Nonlinear Control: Linearization by State Feedback for SISO and MIMO systems, Involutivity, Lie Brackets, Frobenius' Theorem, Zero Dynamics, Inversion, Tracking, Stabilization

• 1/16: Course Outline (PDF)
• 1/16: Lecture Notes 1 (PDF)
• 1/16: Lecture Notes 2 (PDF)
• 1/28: Lecture Notes 3 (PDF)
• 1/30: Lecture Notes 4 (PDF)
• 1/30: Lecture Notes 5 (PDF)
• 2/6: Lecture Notes 6 (PDF)
• 2/6: Lecture Notes 7 (PDF)
• 2/11: Lecture Notes 8 (PDF)
• 2/11: Lecture Notes 9 (PDF)
• 2/13: Lecture Notes 10 (PDF)
• 2/13: Lecture Notes 11 (PDF)
• 2/13: Lecture Notes 12 (PDF)
• 2/24: Lecture Notes 13 (PDF)
• 2/26: Lecture Notes 14 (PDF)
• 3/5: Correction to Lecture Notes 14 (PDF)
• 3/5: Lecture Notes 15 (PDF)
• 3/5: Lecture Notes 16 (PDF)
• 3/5: Lecture Notes 17 (PDF)
• 4/6: Special Lecture on Control Lyapunov Functions (PDF). These are course notes from Professor Koushil Sreenath's 237/222 lectures last Fall, transcribed by Chih-Yuan (Frank) Chiu. The lectures notes were inspired by similar lecture by Professor Jessy Grizzle (U. Michigan).
• 4/6: Lecture Notes 18 (PDF)
• 4/9: Lecture Notes 19 (PDF)
• 4/9: Lecture Notes 20 (PDF)
• 4/23: Lecture Notes 21 (PDF)
• 4/23: Lecture Notes 22 (PDF)
• 4/23: Lecture Notes 23 (PDF)

• 3/10: Recorded Lecture 3/10/20
• 3/12: Recorded Lecture 3/12/20
• 3/17: Recorded Lecture 3/17/20
• 3/19: Recorded Lecture 3/19/20
• 3/31: Recorded Lecture 3/31/20
• 3/31: Captured Zoom slides 3/31/20
• 4/1: Indirect method of Lyapunov, Recorded worked example from Tomlin's office hours
• 4/2: Recorded Lecture 4/2/20
• 4/2: Captured Zoom slides 4/2/20
• 4/7: Recorded Lecture 4/7/20
• 4/7: Captured Zoom slides 4/7/20
• 4/9: Captured Zoom slides 4/9/20
• 4/14: Recorded Lecture 4/14/20
• 4/14: Captured Zoom slides 4/14/20
• 4/16: Recorded Lecture 4/16/20
• 4/16: Captured Zoom slides 4/16/20
• 4/21: Recorded Lecture 4/21/20
• 4/21: Captured Zoom slides 4/21/20
• 4/23: Recorded Lecture 4/23/20
• 4/23: Captured Zoom slides 4/23/20
• 4/28: Recorded Lecture 4/28/20
• 4/28: Captured Zoom slides 4/28/20
• 4/30: Recorded Lecture 4/30/20
• 4/30: Captured Zoom slides 4/30/20

• 1/21: Problem Set 1 (due 1/30) (PDF) (Example MATLAB Script)(Solutions)
• 1/30: Problem Set 2 (due 2/6) (PDF) (Example MATLAB Script) (Solutions)
• 2/6: Problem Set 3 (due 2/13) (PDF) (Solutions)
• 2/13: Problem Set 4 (due 2/21) (PDF) (Solutions)
• 2/24: Problem Set 5 (due 3/3) (PDF) (Solutions)
• 3/11: Problem Set 6 (due 3/20) (PDF) (Solutions)
• 3/20: Problem Set 7 (due 4/2 -- updated due 4/7) (PDF) (Solutions)
• 4/8: Problem Set 8 (due 4/16) (PDF) (Solutions)
• 4/23: Problem Set 9 (due 5/7) (PDF) (Solutions)

• Discussion 1 (PDF) (Solutions)
• Discussion 2 (PDF) (Solutions)
• Discussion 3 (PDF) (Solutions)
• Discussion 4 (PDF) (Solutions)
• Discussion 5 (PDF)
• Discussion 6 (PDF) (Solutions)
• Midterm Review (PDF)(Slides)(Solutions)
• Discussion 7 (PDF) (Note: I didn't release solutions for this -- but you can watch the recorded discussion for a solution)
• Discussion 8 (PDF) (Solutions)
• Discussion 9 (PDF) (Solutions)
• Discussion 10 (PDF) (Solutions)
• Discussion 11 (PDF) (Solutions)
• Discussion 12 (PDF)
• Final Review (PDF) (Solutions)

• 3/13: Recorded Discussion 7
• 4/3: Recorded Discussions 8 and 9
• 4/10: Recorded Discussion 10
• 4/17: Recorded Discussion 11
• 4/24: Recorded Discussion 12
• 5/1: Recorded Discussion 13
• 5/4: Final Review

• Online Controls Tutorial in MATLAB
• MATLAB help for UC Berkeley EECS
• MATLAB Documentation Help Desk
• ODE Software for MATLAB (by Professor Polking at Rice University)

Please sign the handout sheet on the first day of lectures (Tues Jan 21), OR email Professor Tomlin, so that your email will be added to the class mailing list.

Homework 30%
Midterm 30%
Final 40%

The course is based on a set of lecture notes which will be made available throughout the term.
The textbook for the course is:

S. S. Sastry. Nonlinear Systems: Analysis, Stability, and Control. Springer-Verlag, 1999. We will be covering topics from Chapters 1, 2, 5, 9, 10, and selected topics from Chapters 3, 4, and 6.