Linear-quadratic optimal control for infinite-dimensional input-state-output systems
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912160916963328 |
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| author | Reis, Timo Schaller, Manuel |
| author_facet | Reis, Timo Schaller, Manuel |
| contents | We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value is prescribed, we are minimizing over all inputs within a specified convex subset of square integrable controls with values in a Hilbert space. The considered class of infinite-dimensional systems is based on the system node formulation. Thus, our developed approach includes optimal control of a wide variety of linear partial differential equations with boundary control and observation that are not well-posed in the sense that the output continuously depends on the input and the initial value. We provide an application of particular optimal control problems arising in energy-optimal control of port-Hamiltonian systems. Last, we illustrate the our abstract theory by two examples including a non-well-posed heat equation with Dirichlet boundary control and a wave equation on an L-shaped domain with boundary control of the stress in normal direction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11302 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear-quadratic optimal control for infinite-dimensional input-state-output systems Reis, Timo Schaller, Manuel Optimization and Control Functional Analysis 49J20, 49N10, 49K27, 93C25 We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value is prescribed, we are minimizing over all inputs within a specified convex subset of square integrable controls with values in a Hilbert space. The considered class of infinite-dimensional systems is based on the system node formulation. Thus, our developed approach includes optimal control of a wide variety of linear partial differential equations with boundary control and observation that are not well-posed in the sense that the output continuously depends on the input and the initial value. We provide an application of particular optimal control problems arising in energy-optimal control of port-Hamiltonian systems. Last, we illustrate the our abstract theory by two examples including a non-well-posed heat equation with Dirichlet boundary control and a wave equation on an L-shaped domain with boundary control of the stress in normal direction. |
| title | Linear-quadratic optimal control for infinite-dimensional input-state-output systems |
| topic | Optimization and Control Functional Analysis 49J20, 49N10, 49K27, 93C25 |
| url | https://arxiv.org/abs/2401.11302 |