Achieving Precise Mechanical Control in Intrinsically Noisy Systems

TL;DR

This paper develops a theoretical framework for achieving precise control in noisy systems, showing sub-Poisson noise enables control precision, exemplified in biological neuron-like signals for arm movement.

Contribution

It introduces a novel theoretical approach that characterizes control signals as stochastic processes and demonstrates sub-Poisson noise enables precise control in noisy environments.

Findings

Sub-Poisson noise allows for precise control in signal-dependent noisy systems.

Control signals with sub-Poisson noise are modeled as rapidly varying stochastic processes.

Biological neuron bursting pulses can be understood as natural control signals with sub-Poisson noise.

Abstract

How can precise control be realised in intrinsically noisy systems? Here, we develop a general theoretical framework that provides a way to achieve precise control in signal-dependent noisy environments. When the control signal has Poisson or supra-Poisson noise, precise control is not possible. If, however, the control signal has sub-Poisson noise, then precise control is possible. For this case, the precise control solution is not a function, but a rapidly varying random process that must be averaged with respect to a governing probability density functional. Our theoretical approach is applied to the control of straight-trajectory arm movement. Sub-Poisson noise in the control signal is shown to be capable of leading to precise control. Intriguingly, the control signal for this system has a natural counterpart, namely the bursting pulses of neurons --trains of Dirac-delta functions-- in biological systems to achieve precise control performance.