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

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...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: Petri, E, Scheres, K J A, Steur, E, W P M H Heemels
Format: Article
Language:English
Subjects:
Closed loops
Control systems design
Controllers
Dwell time
Feedback control
Hybrid systems
Linear systems
SISO (control systems)
Spiking
Systems analysis
Time invariant systems
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Summary: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.
ISSN:2331-8422