Event-Triggered Control of Neuron Growth with Actuation at Soma
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910369942863872 |
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| author | Demir, Cenk Koga, Shumon Krstic, Miroslav |
| author_facet | Demir, Cenk Koga, Shumon Krstic, Miroslav |
| contents | We introduce a dynamic event-triggering mechanism for regulating the axonal growth of a neuron. We apply boundary actuation at the soma (the part of a neuron that contains the nucleus) and regulate the dynamics of tubulin concentration and axon length. The control law is formulated by applying a Zero-Order Hold (ZOH) to a continuous-time controller which guides the axon to reach the desired length. The proposed dynamic event-triggering mechanism determines the specific time instants at which control inputs are sampled from the continuous-time control law. We establish the existence of a minimum dwell-time between two triggering times that ensures avoidance of Zeno behavior. Through employing the Lyapunov analysis with PDE backstepping, we prove the local stability of the closed-loop system in $L_2$-norm, initially for the target system, and subsequently for the original system. The effectiveness of the proposed method is showcased through numerical simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_00131 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Event-Triggered Control of Neuron Growth with Actuation at Soma Demir, Cenk Koga, Shumon Krstic, Miroslav Optimization and Control We introduce a dynamic event-triggering mechanism for regulating the axonal growth of a neuron. We apply boundary actuation at the soma (the part of a neuron that contains the nucleus) and regulate the dynamics of tubulin concentration and axon length. The control law is formulated by applying a Zero-Order Hold (ZOH) to a continuous-time controller which guides the axon to reach the desired length. The proposed dynamic event-triggering mechanism determines the specific time instants at which control inputs are sampled from the continuous-time control law. We establish the existence of a minimum dwell-time between two triggering times that ensures avoidance of Zeno behavior. Through employing the Lyapunov analysis with PDE backstepping, we prove the local stability of the closed-loop system in $L_2$-norm, initially for the target system, and subsequently for the original system. The effectiveness of the proposed method is showcased through numerical simulations. |
| title | Event-Triggered Control of Neuron Growth with Actuation at Soma |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2310.00131 |