Instructor: Salvatore Monaco, Mattia Mattioni
Course web page: https://elearning.uniroma1.it/course/view.php?id=13733
Credits: 12
Infostud code: 10596147

Objectives

To provide a deeper understanding and to extend system analysis and control design methods proposed in the basic courses on linear systems and control to dynamical systems described by multivariable, nonlinear models that are affine in the input.

Program

Classification issues: From linear to nonlinear state space representations. Input-output properties of input affine systems. The geometry of dynamical systems: From linear to nonlinear. The differential-geometric point of view in the analysis of nonlinear systems: Vector fields and distributions, Frobenius theorem, coordinates transformations and local decompositions. Introduction to stability: Lyapunov general method, LaSalle theorem, the analysis of the linear approximation. Simplification methods: center manifold and Poincaré normal form.
Basics on the geometric approach fro the study of MIMO control systems. Introduction to the control of state affine dynamical systems. Linearization under static and dynamic feedback; disturbance and input-output decoupling problems; dynamical inversion. The concept of zero-dynamics and its role in the stability of feedback control systems. Trajectory and model tracking. From passivity-based concepts to step-by-step methods for feedback stabilization. Application to control problems for mechanical systems.

Type of exam: Written test, Oral test

Reference texts

• S. Monaco, Lecture Notes (to be downloaded from the course web site)
• H.K. Khalil, Nonlinear Systems, 3rd Edition, Prentice Hall, 2002
• A. Isidori, Nonlinear Control Systems, 3rd Edition, Springer, 1995
Further reading:
• S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer, 2003
• H. Nijmeijer and A. Van der Schaft, Nonlinear Dynamical Control Systems, Springer, 1990