Value functional and optimal feedback control in linear-quadratic optimal control problem for fractional-order system
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929325778927616 |
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| author | Gomoyunov, Mikhail I. |
| author_facet | Gomoyunov, Mikhail I. |
| contents | In this paper, a finite-horizon optimal control problem involving a dynamical system described by a linear Caputo fractional differential equation and a quadratic cost functional is considered. An explicit formula for the value functional is given, which includes a solution of a certain Fredholm integral equation. A step-by-step feedback control procedure for constructing $\varepsilon$-optimal controls with any accuracy $\varepsilon > 0$ is proposed. The basis for obtaining these results is the study of a solution of the associated Hamilton-Jacobi-Bellman equation with so-called fractional coinvariant derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_13998 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Value functional and optimal feedback control in linear-quadratic optimal control problem for fractional-order system Gomoyunov, Mikhail I. Optimization and Control 49N10, 34A08, 49L12, 49N35 In this paper, a finite-horizon optimal control problem involving a dynamical system described by a linear Caputo fractional differential equation and a quadratic cost functional is considered. An explicit formula for the value functional is given, which includes a solution of a certain Fredholm integral equation. A step-by-step feedback control procedure for constructing $\varepsilon$-optimal controls with any accuracy $\varepsilon > 0$ is proposed. The basis for obtaining these results is the study of a solution of the associated Hamilton-Jacobi-Bellman equation with so-called fractional coinvariant derivatives. |
| title | Value functional and optimal feedback control in linear-quadratic optimal control problem for fractional-order system |
| topic | Optimization and Control 49N10, 34A08, 49L12, 49N35 |
| url | https://arxiv.org/abs/2208.13998 |