Dynamical Spiking Networks for Distributed Control of Nonlinear Systems

A topic of interest in theoretical neuroscience pertains to understanding how the activity of spiking neural networks (SNNs, i.e., networks of neurons in the brain) is decoded towards enabling control actions. For example, networks in the brain, while complex and stochastic, are nevertheless able to produce reliable and robust motor commands (moving limbs, etc.). To investigate how spiking networks might achieve these goals, we approach the issue from an engineering viewpoint and ask whether it is possible to synthesize such networks for a tracking objective for nonlinear systems. Our approach consists of two nested optimization problems. The inner optimization involves linearization of a nonlinear system about a template trajectory, which enables the synthesis of a control signal via linear optimal control design methods. The outer optimization involves tailoring the spiking of the designed network to 'copy' the constructed optimal control signal. Remarkably, these nested optimization problems can be achieved by a single, recurrent spiking network whose dynamics can be specified in the closed form. Features of the network and examples of its performance are highlighted.