The objective of the course is to convey to students the main notions for systems analysis nonlinear dynamics using tools from systems and control theory. The theoretical tools will be illustrated using engineering examples. Subsequently, the main techniques for the design of controllers for nonlinear systems, based on the project requirements, will be presented.
Course Prerequisites
Basic knowledge of maths, computer science, system and control theory for linear systems.
Teaching Methods
Lectures (hours/year in lecture theatre): 45 Practical class (hours/year in lecture theatre): 0 Practicals / Workshops (hours/year in lecture theatre): 0
Assessment Methods
Closed-book, closed-note written exam. Both knowledge of theory and skills in solving simple exercises will be tested.
Texts
Lecture notes.
Slides used during lectures.
Recorded videos of lectures.
A. Ferrara, M. Cucuzzella, G. P. Incremona, Advanced and Optimization Based Sliding Mode Control: Theory and Application, Series: Advances in Design and Control, SIAM, 2019 (in English).
H.K. Khalil. Nonlinear systems - third edition. Prentice-Hall, 2002 (in English).
S. Sastry. Nonlinear systems - Analysis, Stability and Control. Springer (in English).
Contents
INTRODUCTION TO NON-LINEAR PHENOMENA. Multiple equilibria, limit cycles, sub-harmonics, complex dynamics and chaos. SECOND ORDER SYSTEMS ANALYSIS. The phase plan. Analysis in normal coordinates and Jordan forms. Classification of equilibria. Hartman- Grobman theorem. Closed orbits. Bendixson criterion. Invariant set theorem. Poincaré-Bendixon theorem. Limit cycles. STABILITY THEORY. Lyapunov functions: stability and instability results. Global stability analysis. LaSalle's theorems: Local LaSalle theorem and Global LaSalle theorem. Lyapunov theory for LTI systems: Lyapunov theorem for LTI systems; Global asymptotic stability and global exponential stability of LTI systems. NON-LINEAR CONTROL TECHNIQUES. Linearization-based state feedback control of nonlinear systems: Eigenvalues Assignment problem; Ackermann's formula; regulation of nonlinear systems based on linearization. Variable structure control and sliding mode control: basic concepts, existence of sliding modes, finite time convergence (reaching condition), types of variable structure control laws, design of the sliding manifold for nonlinear systems in different canonical forms. Integral Control, Integral Control via Linearization, Lyapunov-based Control Design, Nonlinear damping, Backstepping, Feedback Linearization, Passivity and Passivity-based Control.
