Nonlinear Control Systems

PhD course, Fall 2021

Lecturer and examinator:

Claudio Altafini (ISY) claudio.altafini@liu.se

Aim:

The course aims at giving an overview of the main control problems and of some of the mathematical tools required in the analysis and synthesis of nonlinear control systems.

Organization

10-12 lectures (2h each, once/twice a week). Lectures in hybrid mode (in person + via zoom).

Schedule

Start: second half of October; End: early December.

• Lecture 1: Tuesday 19th October, at 13:15 in Nollstallet
• Lecture 2: Friday 22nd October, at 13:15 in Nollstallet
• Lecture 3: Friday 29th October, at 10:15 in Systemet
• Lecture 4: Tuesday 2nd November, at 13:15 in Systemet
• Lecture 5: Friday 5th November, at 10:15 in Systemet
• Lecture 6: Tuesday 9th November, at 13:15 in Systemet
• Homework session 1: Friday 12th November, at 10:15 in Systemet
• Lecture 7: Tuesday 16th November, at 13:15 in Systemet
• Lecture 8: Friday 19th November, at 10:15 in Systemet
• Lecture 9: Tuesday 23rd November, at 13:15 in Systemet
• Homework session 2: Friday 26th November, at 10:15 in Systemet
• Lecture 10: Tuesday 30th November, at 13:15 in Systemet
• Lecture 11: Friday 3rd December, at 10:15 in Systemet
• Lecture 12: Tuesday 7th December, at 13:15 in Systemet
• Homework session 3: Friday 10th December, at 10:15 in Systemet

Prerequisites:

Knowledge in Linear Algebra, Automatic Control, Linear System Theory (basic or advanced) is assumed.

Exam:

Hand-in exercises during the course, plus (optional) final take home exam. Credits: 6+3 p

Topics (tentative):

• Lyapunov stability
  • Lyapunov direct method;
  • La Salle invariance principle;
  • stability by linearization;
  • stability of nonautonomous systems;
  • converse theorems.
• Nonlinear controllability
  • differential geometric tools: manifolds, vector fields, Lie backets, Frobenius Theorem;
  • controllablity and Chow Theorem;
  • drift versus driftless systems, accessibility versus controllability;
  • system inversion and differential flatness
• Feedback linearization
  • state linearization;
  • feedback linearization;
  • application to feedback stabilization, output tracking and disturbance decoupling

Course material:

There is no single book covering all material that will be treated in the course. Some parts can be found in the following:

• H. Khalil. Nonlinear Systems, 3rd ed. Prentice Hall. 2002. (stability and stabilization)
• Murray-Li-Sastry. A mathematical Introduction to Robotic Manipulation CRC press 1994. (Controllability; nonholonomic systems; Lie algebras)
• F. Ticozzi. Nonlinear Systems and Control, Lecture Notes, 2019.

My handwritten notes are also available (thanks to Per Bostrom)

• Part 1: Stability of nonlinear systems: part 1.1, part 1.2, part 1.3, part 1.4, part 1.5
• Part 2: Controllability and motion planning part 2.1, part 2.2, part 2.3, part 2.4
• Part 3: Feedback linearization part 3.1, part 3.2, part 3.3.

Informationsansvarig: Claudio Altafini
Senast uppdaterad: 2021-10-19