Spectrum Assignment of Stochastic Systems with Multiplicative Noise
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910902703357952 |
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| author | Xue, Xiaomin Xu, Juanjuan Zhang, Huanshui |
| author_facet | Xue, Xiaomin Xu, Juanjuan Zhang, Huanshui |
| contents | This paper studies the spectrum assignment of a class of stochastic systems with multiplicative noise. A novel $α$-spectrum assignment is proposed for discrete-time and continuous-time stochastic systems with multiplicative noise. In particular, $0$-spectrum assignment is equivalent to the pole assignment for the deterministic systems. The main contribution is two-fold: On the one hand, we present the conditions for $α$-spectrum assignment and the design of feedback controllers based on the system parameters. On the other hand, when the system parameters are unknown, we present a stochastic approximation algorithm to learn the feedback gains which guarantee the spectrum of the stochastic systems to achieve the predetermined value. Numerical examples are provided to demonstrate the effectiveness of the proposed algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02562 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectrum Assignment of Stochastic Systems with Multiplicative Noise Xue, Xiaomin Xu, Juanjuan Zhang, Huanshui Optimization and Control This paper studies the spectrum assignment of a class of stochastic systems with multiplicative noise. A novel $α$-spectrum assignment is proposed for discrete-time and continuous-time stochastic systems with multiplicative noise. In particular, $0$-spectrum assignment is equivalent to the pole assignment for the deterministic systems. The main contribution is two-fold: On the one hand, we present the conditions for $α$-spectrum assignment and the design of feedback controllers based on the system parameters. On the other hand, when the system parameters are unknown, we present a stochastic approximation algorithm to learn the feedback gains which guarantee the spectrum of the stochastic systems to achieve the predetermined value. Numerical examples are provided to demonstrate the effectiveness of the proposed algorithms. |
| title | Spectrum Assignment of Stochastic Systems with Multiplicative Noise |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.02562 |