Funnel control with input filter for nonlinear systems of relative degree two

We address the problem of output reference tracking for unknown nonlinear multi-input, multi-output systems with relative degree two and bounded-input bounded-state (BIBS) stable internal dynamics. We propose a novel model-free adaptive controller that ensures the evolution of the tracking error within prescribed performance funnel boundaries. By applying an output filter, the control objective is achieved without utilizing derivative information of system’s output. The controller is illustrated by a numerical example.

💡 Research Summary

The paper tackles the challenging problem of output‑reference tracking for unknown nonlinear multi‑input multi‑output (MIMO) systems whose relative degree is two. Classical funnel control guarantees that the tracking error stays inside a prescribed performance funnel, but it traditionally requires the availability of higher‑order output derivatives, which are difficult to obtain in practice due to noise amplification and the need for high‑gain observers. To overcome this limitation, the authors propose a novel, model‑free adaptive controller that eliminates the need for any output derivative by introducing a first‑order input filter.

System class. The considered plant is described by
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