Reachability and Controllability Analysis of the State Covariance for Linear Stochastic Systems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911162375864320 |
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| author | Liu, Fengjiao Tsiotras, Panagiotis |
| author_facet | Liu, Fengjiao Tsiotras, Panagiotis |
| contents | This paper studies the set of terminal state covariances that are reachable over a finite time horizon from a given initial state covariance for a linear stochastic system with additive noise. For discrete-time systems, a complete characterization of the set of reachable state covariances is given. For continuous-time systems, we present an upper bound on the set of reachable state covariances. Moreover, for both linear discrete-time and continuous-time systems, necessary and sufficient conditions are provided for the controllability of the state covariance over a finite horizon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14740 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reachability and Controllability Analysis of the State Covariance for Linear Stochastic Systems Liu, Fengjiao Tsiotras, Panagiotis Systems and Control This paper studies the set of terminal state covariances that are reachable over a finite time horizon from a given initial state covariance for a linear stochastic system with additive noise. For discrete-time systems, a complete characterization of the set of reachable state covariances is given. For continuous-time systems, we present an upper bound on the set of reachable state covariances. Moreover, for both linear discrete-time and continuous-time systems, necessary and sufficient conditions are provided for the controllability of the state covariance over a finite horizon. |
| title | Reachability and Controllability Analysis of the State Covariance for Linear Stochastic Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2406.14740 |