An exact active sensing strategy for a class of bio-inspired systems

TL;DR

This paper introduces a biologically inspired active sensing control strategy for translation-invariant systems with nonlinear outputs, demonstrating the emergence of stable limit cycles where traditional feedback fails.

Contribution

It proposes a novel control scheme combining periodic forcing and nonlinear feedback to achieve stability in systems where no static feedback can stabilize.

Findings

The control scheme induces exponentially stable limit cycles.

No dynamic output feedback alone can stabilize these systems.

The approach models biological active sensing behaviors.

Abstract

We consider a general class of translation-invariant systems with a specific category of output nonlinearities motivated by biological sensing. We show that no dynamic output feedback can stabilize this class of systems to an isolated equilibrium point. To overcome this fundamental limitation, we propose a simple control scheme that includes a low-amplitude periodic forcing function akin to so-called "active sensing" in biology, together with nonlinear output feedback. Our analysis shows that this approach leads to the emergence of an exponentially stable limit cycle. These findings offer a provably stable active sensing strategy and may thus help to rationalize the active sensing movements made by animals as they perform certain motor behaviors.