On Hamilton-Jacobi Approaches to State Reconstruction for Dynamic Systems
We investigate the use of Hamilton-Jacobi approaches for the purpose of state reconstruction of dynamic systems. First, the classical formulation based on the minimization of an estimation functional is analyzed. Second, the structure of the resulting estimator is taken into account to study the glo...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/9643291 |
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| _version_ | 1849690384123297792 |
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| author | A. Alessandri |
| author_facet | A. Alessandri |
| author_sort | A. Alessandri |
| collection | DOAJ |
| description | We investigate the use of Hamilton-Jacobi approaches for the purpose of state reconstruction of dynamic systems. First, the classical formulation based on the minimization of an estimation functional is analyzed. Second, the structure of the resulting estimator is taken into account to study the global stability properties of the estimation error by relying on the notion of input-to-state stability. A condition based on the satisfaction of a Hamilton-Jacobi inequality is proposed to construct estimators with input-to-state stable dynamics of the estimation error, where the disturbances affecting such dynamics are regarded as input. Third, the so-developed general framework is applied to the special case of high-gain observers for a class of nonlinear systems. |
| format | Article |
| id | doaj-art-ef92e7c3a26c403fa9da8c930f87f9f6 |
| institution | DOAJ |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-ef92e7c3a26c403fa9da8c930f87f9f62025-08-20T03:21:19ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/96432919643291On Hamilton-Jacobi Approaches to State Reconstruction for Dynamic SystemsA. Alessandri0University of Genoa (DIME), ItalyWe investigate the use of Hamilton-Jacobi approaches for the purpose of state reconstruction of dynamic systems. First, the classical formulation based on the minimization of an estimation functional is analyzed. Second, the structure of the resulting estimator is taken into account to study the global stability properties of the estimation error by relying on the notion of input-to-state stability. A condition based on the satisfaction of a Hamilton-Jacobi inequality is proposed to construct estimators with input-to-state stable dynamics of the estimation error, where the disturbances affecting such dynamics are regarded as input. Third, the so-developed general framework is applied to the special case of high-gain observers for a class of nonlinear systems.http://dx.doi.org/10.1155/2020/9643291 |
| spellingShingle | A. Alessandri On Hamilton-Jacobi Approaches to State Reconstruction for Dynamic Systems Advances in Mathematical Physics |
| title | On Hamilton-Jacobi Approaches to State Reconstruction for Dynamic Systems |
| title_full | On Hamilton-Jacobi Approaches to State Reconstruction for Dynamic Systems |
| title_fullStr | On Hamilton-Jacobi Approaches to State Reconstruction for Dynamic Systems |
| title_full_unstemmed | On Hamilton-Jacobi Approaches to State Reconstruction for Dynamic Systems |
| title_short | On Hamilton-Jacobi Approaches to State Reconstruction for Dynamic Systems |
| title_sort | on hamilton jacobi approaches to state reconstruction for dynamic systems |
| url | http://dx.doi.org/10.1155/2020/9643291 |
| work_keys_str_mv | AT aalessandri onhamiltonjacobiapproachestostatereconstructionfordynamicsystems |