Self-triggered Stabilization of Contracting Systems under Quantization
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909567653249024 |
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| author | Wakaiki, Masashi |
| author_facet | Wakaiki, Masashi |
| contents | We propose self-triggered control schemes for nonlinear systems with quantized state measurements. Our focus lies on scenarios where both the controller and the self-triggering mechanism receive only the quantized state at each sampling time. We assume that the ideal closed-loop system without quantization or self-triggered sampling is contracting. Moreover, an upper bound on the growth rate of the open-loop system is assumed to be known. We present two control schemes that achieve closed-loop stability without Zeno behavior. The first scheme is implemented under logarithmic quantization and uses the quantized state for the threshold in the triggering condition. The second one is a joint design of zooming quantization and self-triggered sampling, where the adjustable zoom parameter for quantization changes based on inter-sampling times and is also used for the threshold of self-triggered sampling. In both schemes, the self-triggering mechanism predicts the future state from the quantized data for the computation of the next sampling time. We employ a trajectory-based approach for stability analysis, where contraction theory plays a key role. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07952 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Self-triggered Stabilization of Contracting Systems under Quantization Wakaiki, Masashi Optimization and Control Systems and Control We propose self-triggered control schemes for nonlinear systems with quantized state measurements. Our focus lies on scenarios where both the controller and the self-triggering mechanism receive only the quantized state at each sampling time. We assume that the ideal closed-loop system without quantization or self-triggered sampling is contracting. Moreover, an upper bound on the growth rate of the open-loop system is assumed to be known. We present two control schemes that achieve closed-loop stability without Zeno behavior. The first scheme is implemented under logarithmic quantization and uses the quantized state for the threshold in the triggering condition. The second one is a joint design of zooming quantization and self-triggered sampling, where the adjustable zoom parameter for quantization changes based on inter-sampling times and is also used for the threshold of self-triggered sampling. In both schemes, the self-triggering mechanism predicts the future state from the quantized data for the computation of the next sampling time. We employ a trajectory-based approach for stability analysis, where contraction theory plays a key role. |
| title | Self-triggered Stabilization of Contracting Systems under Quantization |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2311.07952 |