NONLINEAR CONTROL SYSTEMS
Learning outcomes of the course unit
The course provides concepts and some fundamental methods for the study of nonlinear dynamical continuous-time systems with special emphasis on stability theory. The presented analysis methods can be applied to a variety of physical and artificial phenomena. In the context of the automation science, some feedback systems will be analyzed also focusing on elementary synthesis procedures for nonlinear control.
Course contents summary
Introduction: Mathematical models and nonlinear phenomena. Examples. Existence and uniqueness of the solutions of state-space nonlinear models. The comparison lemma.
Second-order systems: Qualitative behavior of linear systems. Phase diagrams. Multiple equilibria. Limit cycles. Poincaré-Bendixson criterion. Glimpse on chaos and bifuracations.
Lyapunov stability theory: Autonomous systems. Lyapunov¿s theorem. La Salle¿s invariance principle. Linear systems and linearization. Regions of attraction. Nonautonomous systems and Lyapunov¿s theorems. Linear time-varying systems and linearization. Converse theorems. Boundedness of state motions.
Frequency domain analysis of feedback systems: The describing function method. Common nonlinearities. The extended Nyquist criterion and the orbital stability of limit cycles.
Nonlinear control: The stabilization and tracking problems. The gain-scheduling approach. Lyapunov¿s methods. Feedback linearization and the zero dynamics.
1) Lecture notes.
2) H.J. Marquez ¿ Nonlinear control systems: analysis and design, Wiley, 2003.
3) H.K. Khalil ¿ Nonlinear Systems. Third edition. Prentice-Hall, 2002.
4) J.-J. E. Slotine, W. Li ¿ Applied Nonlinear Control. Prentice-Hall, 1991.
Oral lessons and exercitations both at the blackboard and at the computer lab (using MATLAB and Simulink).
Final written tests and oral exam.