Inverse optimal filtering of linear distributed parameter systems
A constructive method is developed to design inverse optimal filters to estimate the states of a class of linear distributed parameter systems (DPSs) based on the calculus of variation approach. Inverse optimality guarantees that the cost functional to be minimized is meaningful in the sense that th...
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| Format: | Journal Article |
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HIKARI Ltd
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/36433 |
| _version_ | 1848754769163714560 |
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| author | Do, Khac Duc |
| author_facet | Do, Khac Duc |
| author_sort | Do, Khac Duc |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | A constructive method is developed to design inverse optimal filters to estimate the states of a class of linear distributed parameter systems (DPSs) based on the calculus of variation approach. Inverse optimality guarantees that the cost functional to be minimized is meaningful in the sense that the symmetric and positive definite weighting kernel matrix on the states is chosen after the filter design instead of being specified at the start of the filter design. Inverse optimal design enables that the Riccati nonlinear partial differential equation (PDE) can be simplified to a Bernoulli PDE, which can be solved analytically. The filter design is based on a new Green matrix formula, a new unique and bounded solution of a linear PDE, and analytical solution of a Bernoulli PDE. The inverse optimal filter design is first developed for the case where the measurements are spatially available, then is extended to the practical case where only a finite number of measurements is available. |
| first_indexed | 2025-11-14T08:45:40Z |
| format | Journal Article |
| id | curtin-20.500.11937-36433 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:45:40Z |
| publishDate | 2013 |
| publisher | HIKARI Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-364332017-10-02T02:28:10Z Inverse optimal filtering of linear distributed parameter systems Do, Khac Duc Distributed parameter systems Inverse optimal filter Riccati PDE Bernoulli PDE A constructive method is developed to design inverse optimal filters to estimate the states of a class of linear distributed parameter systems (DPSs) based on the calculus of variation approach. Inverse optimality guarantees that the cost functional to be minimized is meaningful in the sense that the symmetric and positive definite weighting kernel matrix on the states is chosen after the filter design instead of being specified at the start of the filter design. Inverse optimal design enables that the Riccati nonlinear partial differential equation (PDE) can be simplified to a Bernoulli PDE, which can be solved analytically. The filter design is based on a new Green matrix formula, a new unique and bounded solution of a linear PDE, and analytical solution of a Bernoulli PDE. The inverse optimal filter design is first developed for the case where the measurements are spatially available, then is extended to the practical case where only a finite number of measurements is available. 2013 Journal Article http://hdl.handle.net/20.500.11937/36433 10.12988/ams.2013.37361 HIKARI Ltd fulltext |
| spellingShingle | Distributed parameter systems Inverse optimal filter Riccati PDE Bernoulli PDE Do, Khac Duc Inverse optimal filtering of linear distributed parameter systems |
| title | Inverse optimal filtering of linear distributed parameter systems |
| title_full | Inverse optimal filtering of linear distributed parameter systems |
| title_fullStr | Inverse optimal filtering of linear distributed parameter systems |
| title_full_unstemmed | Inverse optimal filtering of linear distributed parameter systems |
| title_short | Inverse optimal filtering of linear distributed parameter systems |
| title_sort | inverse optimal filtering of linear distributed parameter systems |
| topic | Distributed parameter systems Inverse optimal filter Riccati PDE Bernoulli PDE |
| url | http://hdl.handle.net/20.500.11937/36433 |