Neuro-mechanical control using differential stochastic operators

In order to understand how populations of neurons control movement, several phenomena beyond the realm of classical control theory must be addressed. These include the effect of variability in control due to stochastic firing, the effect of large partially unlabeled cooperative controllers, the effect of bandlimited control due to finite neural resources, and the effect of variation in the number of available neurons. I propose to use differential stochastic operators to model the time-varying effect of multiple stochastic controllers. Integration of these operators yields the time evolution of the probability density of the state. The main result is that since these operators are linear, the combined dynamic effect of populations of neurons can be described by linear combinations of the operators for individual neurons. This permits prediction of the effect of changes in the firing pattern of neurons, and control can be achieved by changing the firing rates of different neurons in a population. The mathematical formulation permits prediction of uncertainty and variability in control, and it also permits prediction of the effect of increase (growth) or decrease (injury) in the number of neurons on the accuracy and stability of control. The theory provides a strong mathematical link between the behavior of individual neurons and populations of neurons, and the dynamic behavior of neuro-mechanical systems.