Funnel control by induced contraction

Abstract

This note explores a property of the internal dynamics that is essential for the functioning of classical funnel control. We relax the property of internal dynamics bounded-input bounded-output (BIBO) stability by concentrating on a narrower class of output reference trajectories. Our ideas have a connection with the recently introduced concept of induced contraction, which is motivated by the phenomenon of noise-induced synchronization in neuronal oscillators. We remark that, contrary to previous works, we only have to modify the class of admissible output reference trajectories to handle non-minimum phase systems. We also propose a way (specific to nonlinear systems) to choose an output reference trajectory (possibly under output constraints) for classical funnel control to work for a certain class of unknown systems.