Funnel control for nonlinear systems with known strict relative degree

We consider tracking control for nonlinear multi-input, multi-output systems which have arbitrary strict relative degree and stable internal dynamics. For a given sufficiently smooth reference signal, our aim is to design a controller which achieves that the tracking error evolves within a prespecified performance funnel. 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. We further present some simulations where our funnel controller is applied to a mechanical system with higher relative degree and compare it with other approaches.