An observability result related to active sensing

TL;DR

This paper establishes necessary and sufficient conditions for global observability in a class of nonlinear, translationally invariant systems, shedding light on active sensing behaviors in biological systems despite their nonlinearity.

Contribution

It provides a novel observability criterion for a broad class of nonlinear systems and links active sensing to maintaining observability in biological contexts.

Findings

Identifies conditions for global observability in nonlinear systems

Shows active sensing helps maintain observability in biological systems

Highlights the role of high-pass sensor dynamics in nonlinear observability

Abstract

For a general class of translationally invariant systems with a specific category of nonlinearity in the output, this paper presents necessary and sufficient conditions for global observability. Critically, this class of systems cannot be stabilized to an isolated equilibrium point by dynamic output feedback. These analyses may help explain the active sensing movements made by animals when they perform certain motor behaviors, despite the fact that these active sensing movements appear to run counter to the primary motor goals. The findings presented here establish that active sensing underlies the maintenance of observability for such biological systems, which are inherently nonlinear due to the presence of the high-pass sensor dynamics.