Input-Constrained Funnel Control of Nonlinear Systems

We study tracking control for uncertain nonlinear multi-input, multi-output systems modeled by
$r$
th order functional differential equations (encompassing systems with arbitrary strict relative degree) in the presence of input constraints. The objective is to guarantee the evolution of the tracking error within a performance funnel with prescribed asymptotic shape (thus achieving desired transient and asymptotic accuracy objectives), for any sufficiently smooth reference signal. We design a novel funnel controller which, in order to satisfy the input constraints, contains a dynamic component, which widens the funnel boundary whenever the input saturation is active. This design is model-free, of low-complexity and extends earlier funnel control approaches. We present a simulation where the controller is compared with these approaches.