Funnel control for nonlinear systems with higher relative degree

Abstract

We consider tracking control for nonlinear multi-input, multi-output systems which have arbitrary strict relative degree and input-to-state stable internal dynamics. For a given reference signal, our aim is to design a controller which achieves that the tracking error evolves within a prespecified performance funnel around the reference signal. To this end, we introduce a new controller which involves the first r − 1 derivatives of the tracking error, where r is the strict relative degree of the system.

Adaptive output error feedback for a class of nonlinear infinite-dimensional systems

“…More recently, funnel control has also been applied to a nonlinear infinite-dimensional reaction-diffusion equation coupled with the nonlinear Fitzhugh-Nagumo model, which represent together defibrillation processes of the human heart, see Berger et al (2021a). Note also that funnel control has been lately coupled to model-predictive-control (Funnel MPC) for nonlinear systems with relative degree one, see Berger et al (2021b).…”