Analysis of a Simple Neuromorphic Controller for Linear Systems: A Hybrid Systems Perspective

TL;DR

This paper presents a hybrid systems analysis of a neuromorphic leaky integrate-and-fire controller for linear systems, demonstrating stability and spike timing properties through a hybrid modeling framework.

Contribution

It introduces a novel hybrid modeling approach for analyzing a neuromorphic controller with stability and dwell-time guarantees for linear systems.

Findings

Proves practical stability of the closed-loop system.

Ensures positive dwell-time between spikes.

Provides parameter relations for neuron dynamics.

Abstract

In this paper we analyze a neuromorphic controller, inspired by the leaky integrate-and-fire neuronal model, in closed-loop with a single-input single-output linear time-invariant system. The controller consists of two neuron-like variables and generates a spiking control input whenever one of these variables reaches a threshold. The control input is different from zero only at the spiking instants and, hence, between two spiking times the system evolves in open-loop. Exploiting the hybrid nature of the integrate-and-fire neuronal dynamics, we present a hybrid modeling framework to design and analyze this new controller. In the particular case of single-state linear time-invariant plants, we prove a practical stability property for the closed-loop system, we ensure the existence of a strictly positive dwell-time between spikes, and we relate these properties to the parameters in the neurons. The results are illustrated in a numerical example.