Controle de sistemas não lineares baseado em dados utilizando o lema de Petersen e uma estratégia iterativa Sum-of-Squares (SOS)

Abstract

The design of control laws for nonlinear dynamical systems is an increasingly challenging task that holds relevance and prominence in control engineering. The study of system’s stability plays a fundamental role in understanding them and, consequently, coping with methods able to stabilize control near desired operation points. In this context, we considered Lyapunov’s stability approach in this work to devise controllers for a buck converter and Van der Pol’s oscillator. In both applications a data-driven strategy was applied, where Petersen’s lemma is vital in finding a Lyapunov condition for asymptotic stability. We conducted system analysis and controller synthesis via SOSTools, a MATLAB toolbox that employs a sum-of- squares approach to solve matrix inequalities.