Non-Asymptotic State-Space Identification of Closed-Loop Stochastic Linear Systems using Instrumental Variables
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911910238093312 |
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| author | Szentpéteri, Szabolcs Csáji, Balázs Csanád |
| author_facet | Szentpéteri, Szabolcs Csáji, Balázs Csanád |
| contents | The paper suggests a generalization of the Sign-Perturbed Sums (SPS) finite sample system identification method for the identification of closed-loop observable stochastic linear systems in state-space form. The solution builds on the theory of matrix-variate regression and instrumental variable methods to construct distribution-free confidence regions for the state-space matrices. Both direct and indirect identification are studied, and the exactness as well as the strong consistency of the construction are proved. Furthermore, a new, computationally efficient ellipsoidal outer-approximation algorithm for the confidence regions is proposed. The new construction results in a semidefinite optimization problem which has an order-of-magnitude smaller number of constraints, as if one applied the ellipsoidal outer-approximation after vectorization. The effectiveness of the approach is also demonstrated empirically via a series of numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_12537 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-Asymptotic State-Space Identification of Closed-Loop Stochastic Linear Systems using Instrumental Variables Szentpéteri, Szabolcs Csáji, Balázs Csanád Systems and Control Dynamical Systems Methodology The paper suggests a generalization of the Sign-Perturbed Sums (SPS) finite sample system identification method for the identification of closed-loop observable stochastic linear systems in state-space form. The solution builds on the theory of matrix-variate regression and instrumental variable methods to construct distribution-free confidence regions for the state-space matrices. Both direct and indirect identification are studied, and the exactness as well as the strong consistency of the construction are proved. Furthermore, a new, computationally efficient ellipsoidal outer-approximation algorithm for the confidence regions is proposed. The new construction results in a semidefinite optimization problem which has an order-of-magnitude smaller number of constraints, as if one applied the ellipsoidal outer-approximation after vectorization. The effectiveness of the approach is also demonstrated empirically via a series of numerical experiments. |
| title | Non-Asymptotic State-Space Identification of Closed-Loop Stochastic Linear Systems using Instrumental Variables |
| topic | Systems and Control Dynamical Systems Methodology |
| url | https://arxiv.org/abs/2301.12537 |