Course content

Methods for analysis and design of nonlinear systems, with an emphasis on nonlinear control systems. The course includes:
1) Mathematical models of nonlinear systems, and fundamental differences between the behavior of linear and nonlinear systems. Equilibrium points, limit cycles and general invariant sets.
2) Phase plane analysis, Lyapunov stability, Input-to-state stability, Input-Output stability, Passivity analysis and the Describing Function Method.
3) Nonlinear control design, including Lyapunov-based control, Energy-based control, Cascaded control, Passivity-based control, Input-Output linearization, and Backstepping.

Learning outcome

Knowledge:
- A thorough knowledge of theory and methods for nonlinear dynamical systems.
- Know how to find the invariant sets of nonlinear dynamical systems, and know how to analyze the system behavior around these sets.
- Know the methods Phase plane analysis, Lyapunov stability analysis, Input-to-state stability, Input-Output stability, Passivity analysis, the Describing Function Method, Lyapunov-based control, Energy-based control, Cascaded control, Passivity-based control, Input-Output linearization, and Backstepping control design.

Skills:
- Proficiency in independently assessing the advantages and disadvantages of the different nonlinear methods, and make a qualified choice of method for analysis and design of a dynamical system.
- Proficiency in independently applying the methods for analysis and design of nonlinear control systems.
- Proficiency in assessing the advantages and limitations of the resulting nonlinear control system.

General competence:
- Skills in applying this knowledge and proficiency in new areas and complete advanced tasks and projects.
- Skills in communicating extensive independent work, and master the technical terms of nonlinear dynamical control systems.
- Ability to contribute to innovative thinking and innovation processes.

Learning methods and activities

Lectures and problem sets. Four out of six assignments must be approved. If there is a re-sit examination, the examination form may be changed from written to oral. The exam is given in English.

Compulsory assignments

• Exercises

Recommended previous knowledge

The courses TTK4105 Control Systems and TTK4115 Linear System Theory, or similar knowledge.

Course materials

Khalil: Nonlinear Systems, 3rd edition, Prentice Hall, 2002. Selected conference and Journal papers.

Credit reductions