Achieving Precise Mechanical Control in Intrinsically Noisy Systems

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.