Proximal observers for secure state estimation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909034307649536 |
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| author | Bako, Laurent Nadri, Madiha Andrieu, Vincent Zhang, Qinghua |
| author_facet | Bako, Laurent Nadri, Madiha Andrieu, Vincent Zhang, Qinghua |
| contents | This paper discusses a general framework for designing robust state estimators for a class of discrete-time nonlinear systems. We consider systems that may be impacted by impulsive (sparse but otherwise arbitrary) measurement noise sequences. We show that a family of state estimators, robust to this type of undesired signal, can be obtained by minimizing a class of nonsmooth convex functions at each time step. The resulting state observers are defined through proximal operators. We obtain a nonlinear implicit dynamical system in term of estimation error and prove, in the noise-free setting, that it vanishes asymptotically when the minimized loss function and the to-be-observed system enjoy appropriate properties. From a computational perspective, even though the proposed observers can be implemented via efficient numerical procedures, they do not admit closed-form expressions. The paper argues that by adopting appropriate relaxations, simple and fast analytic expressions can be derived. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06098 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Proximal observers for secure state estimation Bako, Laurent Nadri, Madiha Andrieu, Vincent Zhang, Qinghua Optimization and Control Systems and Control This paper discusses a general framework for designing robust state estimators for a class of discrete-time nonlinear systems. We consider systems that may be impacted by impulsive (sparse but otherwise arbitrary) measurement noise sequences. We show that a family of state estimators, robust to this type of undesired signal, can be obtained by minimizing a class of nonsmooth convex functions at each time step. The resulting state observers are defined through proximal operators. We obtain a nonlinear implicit dynamical system in term of estimation error and prove, in the noise-free setting, that it vanishes asymptotically when the minimized loss function and the to-be-observed system enjoy appropriate properties. From a computational perspective, even though the proposed observers can be implemented via efficient numerical procedures, they do not admit closed-form expressions. The paper argues that by adopting appropriate relaxations, simple and fast analytic expressions can be derived. |
| title | Proximal observers for secure state estimation |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2401.06098 |