Nonlinear Control Systems

PhD course, Fall 2023

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 person.

Schedule for 2023

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

• Lecture 1: Tuesday 10th October, at 13:15 in Nollstallet
• Lecture 2: Thursday 12th October, at 15:15 in Nollstallet
• Lecture 3: Tuesday 17th October, at 13:15 in Nollstallet
• Lecture 4: Thursday 19th October, at 15:15 in Nollstallet
• Lecture 5: Tuesday 24th October, at 13:15 in Nollstallet
• Lecture 6: Thursday 26th October, at 15:15 in Ljungeln
• Lecture 7: Tuesday 31st October, at 13:15 in Nollstallet
• Homework session 1: Thursday 2nd November, at 15:15 in Nollstallet
• Lecture 8: Tuesday 7th November, at 13:15 in Nollstallet
• Lecture 9: Thursday 9th November, at 15:15 in Nollstallet
• Lecture 10: Tuesday 14rd November, at 13:15 in Nollstallet
• Homework session 2: Thursday 16th November, at 15:15 in Nollstallet
• Lecture 11: Tuesday 21st November, at 13:15 in Nollstallet
• Lecture 12: Thursday 23rd November, at 15:15 in Nollstallet
• Homework session 3: Thursday 30th November, at 15:15 in Nollstallet

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: 2023-10-18