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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.01793 |
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| _version_ | 1866916016566566912 |
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| author | Braghini, Danio Shivakumar, Sachin Peet, Matthew M. |
| author_facet | Braghini, Danio Shivakumar, Sachin Peet, Matthew M. |
| contents | The $H_2$ norm is a commonly used performance metric in the design of estimators. However, $H_2$-optimal estimation of most PDEs is complicated by the lack of transfer function and state-space representations. To address this problem, we first re-characterize the $H_2$-norm in terms of a map from initial condition to output. We then leverage the Partial Integral Equation (PIE) state-space representation of systems of linear PDEs coupled with ODEs to recast this characterization of $H_2$-norm as a convex optimization problem defined in terms of Linear Partial Integral (LPI) inequalities. We then parameterize a class of PIE-based observers and solve the associated $H_2$-optimal estimation problem. The observer synthesis problem is then recast as an LPI, and the resulting observers are validated using numerical simulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01793 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $H_2$-Optimal Estimation of Linear Delayed and PDE Systems Braghini, Danio Shivakumar, Sachin Peet, Matthew M. Optimization and Control The $H_2$ norm is a commonly used performance metric in the design of estimators. However, $H_2$-optimal estimation of most PDEs is complicated by the lack of transfer function and state-space representations. To address this problem, we first re-characterize the $H_2$-norm in terms of a map from initial condition to output. We then leverage the Partial Integral Equation (PIE) state-space representation of systems of linear PDEs coupled with ODEs to recast this characterization of $H_2$-norm as a convex optimization problem defined in terms of Linear Partial Integral (LPI) inequalities. We then parameterize a class of PIE-based observers and solve the associated $H_2$-optimal estimation problem. The observer synthesis problem is then recast as an LPI, and the resulting observers are validated using numerical simulation. |
| title | $H_2$-Optimal Estimation of Linear Delayed and PDE Systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2411.01793 |