Top-down modeling of distributed neural dynamics for motion control

In neuroscience a topic of interest pertains to understanding the neural circuit and network mechanisms that enable a range of motor functions, including motion and navigation. While engineers have strong mathematical conceptualizations regarding how these functions can be achieved using control-theoretic frameworks, it is far from clear whether similar strategies are embodied within neural circuits. In this work, we adopt a 'top-down' strategy to postulate how certain nonlinear control strategies might be achieved through the actions of a network of biophysical neurons acting on multiple time-scales. Specifically, we study how neural circuits might interact to learn and execute an optimal strategy for spatial control. Our approach is comprised of an optimal nonlinear control problem where a high-level objective function encapsulates the fundamental requirements of the task at hand. We solve this optimization using an iterative method based on Pontryagin's Maximum Principle. It turns out that the proposed solution methodology can be translated into the dynamics of neural populations that act to produce the optimal solutions in a distributed fashion. Importantly, we are able to provide conditions under which these networks are guaranteed to arrive at an optimal solution. In total, this work provides an iterative optimization framework that confers a novel interpretation regarding how nonlinear control can be achieved in neural circuits.