Iterative approximations of periodic trajectories for nonlinear systems with discontinuous inputs
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908408153636864 |
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| author | Zuyev, Alexander Benner, Peter |
| author_facet | Zuyev, Alexander Benner, Peter |
| contents | Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of Carathéodory solutions. It is shown that, under the dominant linearization assumption, the considered class of boundary value problems admits a unique solution for any admissible control. These solutions can be obtained as the limit of the proposed simple iterative scheme and, in the case of periodic boundary conditions, via the developed Newton-type schemes. Under additional technical assumptions, sufficient contraction conditions of the corresponding generating operators are derived analytically. The proposed iterative approach is applied to compute periodic solutions of a realistic chemical reaction model with discontinuous control inputs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_00310 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Iterative approximations of periodic trajectories for nonlinear systems with discontinuous inputs Zuyev, Alexander Benner, Peter Optimization and Control 93C15, 34B15, 34A36, 47J25, 65L10, 92E20 Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of Carathéodory solutions. It is shown that, under the dominant linearization assumption, the considered class of boundary value problems admits a unique solution for any admissible control. These solutions can be obtained as the limit of the proposed simple iterative scheme and, in the case of periodic boundary conditions, via the developed Newton-type schemes. Under additional technical assumptions, sufficient contraction conditions of the corresponding generating operators are derived analytically. The proposed iterative approach is applied to compute periodic solutions of a realistic chemical reaction model with discontinuous control inputs. |
| title | Iterative approximations of periodic trajectories for nonlinear systems with discontinuous inputs |
| topic | Optimization and Control 93C15, 34B15, 34A36, 47J25, 65L10, 92E20 |
| url | https://arxiv.org/abs/2401.00310 |