nonlinear and adaptive control


The course covers basics of control for systems depending on unknown parameters. The overall goals and course objectives, here.
Prerequisite: ECE515 or instructor’s consent.

who, when, where

lecture: Tu-Th, 2-3:20pm ECE2017. Videos will be available on this channel (sign-in required).

homework etc will be published on gradescope (code NX6W3Y); submit there as well.

schedule (lectures, topics, homework)

  • Tue Aug 22 Introduction and administrivia. Problem setting: systems depending on parameters, feedback control stabilizing them. Archetypal example: \(\dot{y}=\theta y+u\), \(\theta\in{\Real}\). Regulators, tuning laws. Stability, recap on Lyapunov theory. (Script, Sect. 1.)
  • Thu Aug 24 Weak Lyapunov functions. Barbalat lemma. Usage to prove stabilization. Limit sets of dynamical systems, their invariance under the flow. LaSalle-Krasovski. (Script, Sect. 2.2.)
  • Tue Aug 29 Further examples of weak- and pseudo-Lyapunov functions. Connections to observability in linear control. LTV: Uniform Complete Observability condition. (Script, Sect. 2.3.)
    Homework 1
    published: due by the end of 9.8. Solutions.
  • Thu Aug 31 Universal regulation. Impossibility of universal regulators for regulators with finitely many sign changes. Existence of universal regulators with Nussbaum-Willems-Byrnes controllers in univariate case. (Script, Sect. 3.1)
  • Tue Sep 5 Universal regulation, higher dimensions: universal regulators in SISO, relative degree 1, minimal phase case. Estimates on the ( \(L_2\)-operator) norm of the input-output map for stable LTI systems. (Script, Sect. 3.1, 3.3)
  • Thu Sep 7 More on relative degree, zero dynamics and minimal phase systems. (Script, Sect. 3.2)
  • Tue Sep 12 Stabilization of nonlinear mean phase systems. Lyapunov-based design. Some impossibilities. (Script, Sect. 4.1)
  • Thu Sep 14 Universal formula for Lyapunov-based design. (Script, Sect. 4.1)
  • Tue Sep 19 CLFs and adaptive control. Backstepping. (Script, Sect. 4.2, 5.1)
    Homework 2 published, due by the end of 9.28. Solutions.
  • Thu Sep 21 Adaptive backstepping. Optimization tools.(Script, Sect. 5.2, 6.1)
  • Tue Sep 26 Parameter estimation, stable case (Script, Sect. 6.2)
  • Thu Sep 28 Parameter estimation, stable case, arbitrary dimension (Script, Sect. 6.2)
  • Tue Oct 3 Online parameter estimation in SISO (Script, Sect. 6.3)
  • Thu Oct 5 Online parameter estimation in SISO, least squares (Script, Sect. 6.3)
  • Tue Oct 10 Online parameter estimation in SISO, projection (Script, Sect. 6.3).
    Homework 3
  • Thu Oct 12 Rich signals and parameter identification (Script, Sect. 6.3)
  • Tue Oct 17 Model Reference Adaptive Control (MRAC) (Script, Sect. 6.5)
  • Thu Oct 19 Direct and indirect MRAC (Script, Sect. 6.5)
  • Tue Oct 24 Indirect MRAC (Script, Sect. 6.5). Input-to-State Stability (Script, Sect. 7.1).
  • Thu Oct 26 Input-to-State Stability (Script, Sect. 7.2-3).
  • Tue Oct 31 Input-to-State Stability (Script, Sect. 7.3-4).
  • Thu Nov 2 Slowly Varying Systems (Script, Sect. 8.1-2).
    Homework 4
  • Tue Nov 7 Singularly Perturbed Systems (Script, Sect. 10.1-2).
  • Thu Nov 9 Singularly Perturbed Systems (Script, Sect. 10.2-3).
  • Tue Nov 14 Ensemble Control (Script to come).
  • Thu Nov 16 Ensemble Control
  • Fall Break
  • Tue Nov 28 Final presentations
  • Thu Nov 30 Final presentations
  • Tue Dec 5 Wrap-up


final presentation

  • For the presentation, choose a topic related to the course content, understand and critically summarize a paper in that area, and make a fifteen-minute presentation. All presentations will be done online – either during the usual class time Tuesday Nov 28 and Thursday Nov 30, or by arrangement.
    You can work solo, or in groups of 2.
  • You can choose a paper from the list or propose your own. In either case, please send an email to the instructor with your choice of paper and your list of group members as soon as possible, but no later than Tuesday, Nov 14, one email per group. Papers from the list that have already been claimed will be removed.
  • Since the presentation will be limited to fifteen minutes, you should aim to have no more than seven slides and focus on the main idea or theorem in the paper you are presenting. Avoid the temptation to get into lengthy technical details, concentrate on the context instead.
    You should focus on a) presenting the context (general outline of the field, pre-existing results, if the work is old, what happened since), and b) succinctly describing a main finding in the paper: a theorem, an algorithm, including, if possible, key elements of the proofs.
  • Evaluation:
    • context understood – 40%
    • main result internalized – 40%
    • quality of the slides and the presentation – 20%
  • Book your presentation slot here


Academic Integrity

The University of Illinois at Urbana-Champaign Student Code should also be considered as a part of this syllabus. Students should pay particular attention to Article 1, Part 4: Academic Integrity. Read the Code at the following URL:

Academic dishonesty may result in a failing grade. Every student is expected to review and abide by the Academic Integrity Policy: Ignorance is not an excuse for any academic dishonesty. It is your responsibility to read this policy to avoid any misunderstanding. Do not hesitate to ask the instructor(s) if you are ever in doubt about what constitutes plagiarism, cheating, or any other breach of academic integrity.

Emergency Response Recommendations

Emergency response recommendations can be found at the following website: I encourage you to review this website and the campus building floor plans website within the first 10 days of class.

Sexual Misconduct Reporting Obligation

The University of Illinois is committed to combating sexual misconduct. Faculty and staff members are required to report any instances of sexual misconduct to the University’s Title IX Office. In turn, an individual with the Title IX Office will provide information about rights and options, including accommodations, support services, the campus disciplinary process, and law enforcement options.

A list of the designated University employees who, as counselors, confidential advisors, and medical professionals, do not have this reporting responsibility and can maintain confidentiality, can be found here:

Other information about resources and reporting is available here:

Religious Observances

Illinois law requires the University to reasonably accommodate its students’ religious beliefs, observances, and practices in regard to admissions, class attendance, and the scheduling of examinations and work requirements. You should examine this syllabus at the beginning of the semester for potential conflicts between course deadlines and any of your religious observances. If a conflict exists, you should notify your instructor of the conflict and follow the procedure at to request appropriate accommodations. This should be done in the first two weeks of classes.

Disability-Related Accommodations

To obtain disability-related academic adjustments and/or auxiliary aids, students with disabilities must contact the course instructor and the Disability Resources and Educational Services (DRES) as soon as possible. To contact DRES, you may visit 1207 S. Oak St., Champaign, call 333-4603, e-mail or go to If you are concerned you have a disability-related condition that is impacting your academic progress, there are academic screening appointments available that can help diagnosis a previously undiagnosed disability. You may access these by visiting the DRES website and selecting “Request an Academic Screening” at the bottom of the page..

Family Educational Rights and Privacy Act (FERPA)

Any student who has suppressed their directory information pursuant to Family Educational Rights and Privacy Act (FERPA) should self-identify to the instructor to ensure protection of the privacy of their attendance in this course. See for more information on FERPA.

Public Health

Student location address You should insert and/or update your “Student Location” in Student Self-Service every time your living location changes. Typically, this is at the beginning of each academic year but could change throughout the year. 
Maintaining updated location information enables campus health and wellness units to communicate proper protocols to students that will help us all maximize safety during the pandemic.

Feeling ill and absences: Students need to take responsibility for checking their symptoms every day. Students who feel ill must not come to class.  These students are judged to have excused absences for the class period and should contact the instructor via email about making up the work.    

Run > Hide > Fight

Emergencies can happen anywhere and at any time. It is important that we take a minute to prepare for a situation in which our safety or even our lives could depend on our ability to react quickly. When we’re faced with almost any kind of emergency – like severe weather or if someone is trying to hurt you – we have three options: Run, hide or fight.

Run: Leaving the area quickly is the best option if it is safe to do so. Take time now to learn the different ways to leave your building. Leave personal items behind. Assist those who need help, but consider whether doing so puts yourself at risk. Alert authorities of the emergency when it is safe to do so.

Hide: When you can’t or don’t want to run, take shelter indoors. Take time now to learn different ways to seek shelter in your building. If severe weather is imminent, go to the nearest indoor storm refuge area. If someone is trying to hurt you and you can’t evacuate, get to a place where you can’t be seen, lock or barricade your area if possible, silence your phone, don’t make any noise and don’t come out until you receive an Illini-Alert indicating it is safe to do so.

Fight: As a last resort, you may need to fight to increase your chances of survival. Think about what kind of common items are in your area which you can use to defend yourself. Team up with others to fight if the situation allows. Mentally prepare yourself – you may be in a fight for your life.

Please be aware of people with disabilities who may need additional assistance in emergency situations.

Other resources: for more information on how to prepare for emergencies, including how to run, hide or fight and building floor plans that can show you safe areas. to sign up for Illini-Alert text messages.