Toward Neuronal Implementations of Delayed Optimal Control

TL;DR

This paper explores how neural circuits can implement delayed optimal control strategies, specifically linear quadratic regulators, revealing minimal circuit configurations and their firing rate characteristics.

Contribution

It introduces minimal neural circuit configurations capable of implementing delayed linear quadratic regulators, bridging control theory and neural implementation.

Findings

Three minimal neural circuit configurations implement the same controller.

Firing rate characteristics can vary significantly across circuits.

The work bridges controller realizations with neural delay structures.

Abstract

Animal sensorimotor behavior is frequently modeled using optimal controllers. However, it is unclear how the neural circuits within the animal's nervous system implement optimal controller-like behavior. In this work, we study the question of implementing a delayed linear quadratic regulator with linear dynamical "neurons" on a muscle model. We show that for any second-order controller, there are three minimal neural circuit configurations that implement the same controller. Furthermore, the firing rate characteristics of each circuit can vary drastically, even as the overall controller behavior is preserved. Along the way, we introduce concepts that bridge controller realizations to neural implementations that are compatible with known neuronal delay structures.