Funnel control for nonlinear systems with known strict relative degree

We consider tracking control for uncertain nonlinear multi-input, multi-output systems which have arbitrary strict relative degree and input-to-state stable internal dynamics. For a given sufficiently smooth reference signal, our aim is to design a low-complexity model-free 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 derive an explicit bound for the resulting input and discuss the influence of the controller parameters. We further present some simulations where our funnel controller is applied to a mechanical system with higher relative degree and a two-input, two-output robot manipulator. The controller is also compared with other approaches.