  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.
