Analysis of a Simple Neuromorphic Controller for Linear Systems: A Hybrid Systems Perspective
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910597625413632 |
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| author | Petri, E. Scheres, K. J. A. Steur, E. Heemels, W. P. M. H. |
| author_facet | Petri, E. Scheres, K. J. A. Steur, E. Heemels, W. P. M. H. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06353 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analysis of a Simple Neuromorphic Controller for Linear Systems: A Hybrid Systems Perspective Petri, E. Scheres, K. J. A. Steur, E. Heemels, W. P. M. H. Systems and Control 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. |
| title | Analysis of a Simple Neuromorphic Controller for Linear Systems: A Hybrid Systems Perspective |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2409.06353 |