On Data-Driven Stochastic Output-Feedback Predictive Control
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866929575281295360 |
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| author | Pan, Guanru Ou, Ruchuan Faulwasser, Timm |
| author_facet | Pan, Guanru Ou, Ruchuan Faulwasser, Timm |
| contents | The fundamental lemma by Jan C. Willems and co-authors enables the representation of all input-output trajectories of a linear time-invariant system by measured input-output data. This result has proven to be pivotal for data-driven control. Building on a stochastic variant of the fundamental lemma, this paper presents a data-driven output-feedback predictive control scheme for stochastic Linear Time-Invariant (LTI) systems. The considered LTI systems are subject to non-Gaussian disturbances about which only information about their first two moments is known. Leveraging polynomial chaos expansions, the proposed scheme is centered around a data-driven stochastic Optimal Control Problem (OCP). Through tailored online design of initial conditions, we provide sufficient conditions for the recursive feasibility of the proposed output-feedback scheme based on a data-driven design of the terminal ingredients of the OCP. Furthermore, we provide a robustness analysis of the closed-loop performance. A numerical example illustrates the efficacy of the proposed scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_17074 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Data-Driven Stochastic Output-Feedback Predictive Control Pan, Guanru Ou, Ruchuan Faulwasser, Timm Systems and Control Optimization and Control The fundamental lemma by Jan C. Willems and co-authors enables the representation of all input-output trajectories of a linear time-invariant system by measured input-output data. This result has proven to be pivotal for data-driven control. Building on a stochastic variant of the fundamental lemma, this paper presents a data-driven output-feedback predictive control scheme for stochastic Linear Time-Invariant (LTI) systems. The considered LTI systems are subject to non-Gaussian disturbances about which only information about their first two moments is known. Leveraging polynomial chaos expansions, the proposed scheme is centered around a data-driven stochastic Optimal Control Problem (OCP). Through tailored online design of initial conditions, we provide sufficient conditions for the recursive feasibility of the proposed output-feedback scheme based on a data-driven design of the terminal ingredients of the OCP. Furthermore, we provide a robustness analysis of the closed-loop performance. A numerical example illustrates the efficacy of the proposed scheme. |
| title | On Data-Driven Stochastic Output-Feedback Predictive Control |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2211.17074 |