LQ Optimal Control of First-Order Hyperbolic PDE Systems with Final State Constraints
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916491364925440 |
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| author | Xue, Xiaomin Xu, Juanjuan Zhang, Huanshui Hu, Long |
| author_facet | Xue, Xiaomin Xu, Juanjuan Zhang, Huanshui Hu, Long |
| contents | This paper studies the linear-quadratic (LQ) optimal control problem of a class of systems governed by the first-order hyperbolic partial differential equations (PDEs) with final state constraints. The main contribution is to present the solvability condition and the corresponding explicit optimal controller by using the Lagrange multiplier method and the technique of solving forward and backward partial differential equations (FBPDEs). In particular, the result is reduced to the case with zero-valued final state constraints. Several numerical examples are provided to demonstrate the performance of the designed optimal controller. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04537 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | LQ Optimal Control of First-Order Hyperbolic PDE Systems with Final State Constraints Xue, Xiaomin Xu, Juanjuan Zhang, Huanshui Hu, Long Optimization and Control This paper studies the linear-quadratic (LQ) optimal control problem of a class of systems governed by the first-order hyperbolic partial differential equations (PDEs) with final state constraints. The main contribution is to present the solvability condition and the corresponding explicit optimal controller by using the Lagrange multiplier method and the technique of solving forward and backward partial differential equations (FBPDEs). In particular, the result is reduced to the case with zero-valued final state constraints. Several numerical examples are provided to demonstrate the performance of the designed optimal controller. |
| title | LQ Optimal Control of First-Order Hyperbolic PDE Systems with Final State Constraints |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2402.04537 |