Neuromimetic Control — A Linear Model Paradigm

Stylized models of the neurodynamics that under-pin sensory motor control in animals are proposed and studied. The voluntary motions of animals are typically initiated by high level intentions created in the primary cortex through a combination of perceptions of the current state of the environment along with memories of past reactions to similar states. Muscle movements are produced as a result of neural processes in which the parallel activity of large multiplicities of neurons generate signals that collectively lead to desired actions. Essential to coordinated muscle movement are intentionality, prediction, regions of the cortex dealing with misperceptions of sensory cues, and a significant level of resilience with respect to disruptions in the neural pathways through which signals must propagate. While linear models of feedback control systems have been well studied over many decades, this paper proposes and analyzes a class of models whose aims are to capture some of the essential features of neural control of movement. Whereas most linear models of feedback systems entail a state component whose dimension is higher than the number of inputs or outputs, the work that follows will treat models in which the numbers of input and output channels greatly exceed the state dimension. While we begin by considering continuous-time systems governed by differential equations, the aim will be to treat systems whose evolution involves classes of inputs that emulate neural spike trains. Within the proposed class of models, the paper will study resilience to channel dropouts, the ways in which noise and uncertainty can be mitigated by an appropriate notion of consensus among noisy inputs, and finally, by a simple model in which binary activations of a multiplicity of input channels produce a dynamic response that closely approximates the dynamics of a prescribed linear system whose inputs are continuous functions of time.