Göm meny

# Nonlinear Control Systems

## PhD course, Fall 2021

### 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)

Informationsansvarig: Claudio Altafini