Recovering Observability via Active Sensing
Kunapareddy, Abhinav Srinivas Sai Kiran
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Observability is a formal property of a system that ensures the ability to estimate the system’s states from output measurements and knowledge of the inputs. Even when state estimators are not employed, observability is a crucial property in the design of feedback control systems. Engineering sensors are typically designed to guarantee observability irrespective of the control input, thereby simplifying control systems design. Here, we introduce a class of nonlinear sensors that require ‘persistently exciting’ control inputs to maintain observability. This class of sensor models is motivated by biological sensing systems which ‘adapt’ to constant stimuli, giving them a very high dynamic range, but leading to a phenomenon known as perceptual fading. To prevent perceptual fading, animals employ active sensing behaviors in the form of time-varying motor commands that continually stimulate sensory receptors. To capture this phenomenon, we introduce a simplified sensor model that requires similar ‘active’ control inputs to maintain observability. Under certain assumptions, the input–output characteristics of the active sensing system is shown to be equivalent to an observable LTI system. Specifically, we apply three steps to the original (nonlinear) system—(1) modulating via sinusoidal active input, (2) demodulating, and (3) low-pass filtering. The equivalent system is identified by analyzing the Harmonic Transfer Function (HTF) of the modulated system and whose output is then demodulated and low pass filtered. Equivalence of the new observable LTI system and the active sensing system illustrates the potential effectiveness of this framework for active sensing and may pave the way for the design of adaptive sensory systems for engineering applications.