Introduction

Abstract

In this chapter we introduce extremum seeking (ES) as a method for stabilization of unknown, nonlinear, time-varying systems, by utilizing an ES approach directly as the feedback controller itself. Our “extremum seeking for stabilization” (ESS) consists of employing the control Lyapunov function (clf) as the cost function in a slightly modified extremum seeking algorithm. The goal is to minimize the clf, i.e., to drive the clf value to zero over time, which amounts to asymptotic stabilization. Unlike conventional clf-based stabilization approaches, which employ the knowledge of the system model in the feedback law (Sontag’s formula being a ‘universal’ and a particularly clear example of such a feedback law), our ESS approach does not rely on the system model and doesn’t require its knowledge. Instead, ESS employs periodic perturbation signals, along with the clf. The same effect as that of clf-based feedback laws that imply the modeling knowledge is achieved, but in a time-average sense.