Emulation-based Neuromorphic Control for the Stabilization of LTI Systems

TL;DR

This paper introduces a systematic emulation-based method for designing neuromorphic spiking neural network controllers to stabilize LTI systems, ensuring stability and accurate signal emulation.

Contribution

It presents a novel two-step design procedure for SNN controllers and introduces a new stability concept called iSISS, with proofs and practical validation.

Findings

The method guarantees stable control of LTI systems using SNNs.

The emulation accuracy of spike signals can be arbitrarily improved.

The approach is validated through a numerical case study.

Abstract

Brain-inspired neuromorphic technologies can offer important advantages over classical digital clock-based technologies in various domains, including systems and control engineering. Indeed, neuromorphic engineering could provide low-latency, low-energy and adaptive control systems in the form of spiking neural networks (SNNs) exploiting spike-based control and communication. However, systematic methods for designing and analyzing neuron-inspired spiking controllers are currently lacking. This paper presents a new systematic approach for stabilizing linear time-invariant (LTI) systems using SNN-based controllers, designed as a network of integrate-and-fire neurons, whose input is the measured output from the plant and generating spiking control signals. The new approach consists of a two-step emulation-based design procedure. In the first step, we establish conditions on the neuron parameters to ensure that the spiking signal generated by a pair of neurons emulates any continuous-time signal input to the neurons with arbitrary accuracy in terms of a special metric for spiky signals. In the second step, we propose a novel stability notion, called integral spiking-input-to-state stability (iSISS) building on this special metric. We prove that an asymptotically stable LTI system has this iSISS property. By combining these steps, a certifiable practical stability property of the closed-loop system can be established. Generalizations are discussed and the effectiveness of the approach is illustrated in a numerical case study.