1. D. Biswas, E.D Sontag, and N.J. Cowan. An exact active sensing strategy for a class of bio-inspired systems. European Journal of Control, 2025. Note: Also in Proc. 23rd European Control Conference, and longer version in https://arxiv.org/abs/2411.06612.[WWW] [PDF] Keyword(s): active sensing, systems biology, observability, nonlinear control, nonlinear systems, active sensing, weakly electric fish, observability, biological systems, nonlinear system theory, linear time-varying systems. 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.

1. E.D. Sontag, D. Biswas, and N.J. Cowan. An observability result related to active sensing. Technical report, 2022. Note: ArXiv 2210.03848. [PDF] Keyword(s): nonlinear systems, observability, active sensing. 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.

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