Well-posedness and Stability of Discrete Approximations for Controlled Sweeping Processes with Time Delay
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914960766926848 |
|---|---|
| author | Mordukhovich, Boris Nguyen, Dao Nguyen, Trang Ortiz-Robinson, Norma Ríos, Vinicio |
| author_facet | Mordukhovich, Boris Nguyen, Dao Nguyen, Trang Ortiz-Robinson, Norma Ríos, Vinicio |
| contents | This paper addresses, for the first time in the literature, optimal control problems for dynamic systems governed by a novel class of sweeping processes with time delay. We establish well-posedness of such processes, in the sense of the existence and uniqueness of feasible trajectories corresponding to feasible controls under fairly unrestrictive assumptions. Then we construct a well-posed family of discrete approximations and find efficient conditions under the discretized time-delayed sweeping process exhibits stability with respect to strong convergence of feasible and optimal solutions. This creates a bridge between optimization of continuous-time and discrete-time sweeping control systems and justifies the effective use of discrete approximations in deriving optimality conditions and numerical techniques to solve the original time-delayed sweeping control problems via discrete approximations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20404 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness and Stability of Discrete Approximations for Controlled Sweeping Processes with Time Delay Mordukhovich, Boris Nguyen, Dao Nguyen, Trang Ortiz-Robinson, Norma Ríos, Vinicio Optimization and Control 49J24, 49J25, 49J53, 49M25, 93B35 This paper addresses, for the first time in the literature, optimal control problems for dynamic systems governed by a novel class of sweeping processes with time delay. We establish well-posedness of such processes, in the sense of the existence and uniqueness of feasible trajectories corresponding to feasible controls under fairly unrestrictive assumptions. Then we construct a well-posed family of discrete approximations and find efficient conditions under the discretized time-delayed sweeping process exhibits stability with respect to strong convergence of feasible and optimal solutions. This creates a bridge between optimization of continuous-time and discrete-time sweeping control systems and justifies the effective use of discrete approximations in deriving optimality conditions and numerical techniques to solve the original time-delayed sweeping control problems via discrete approximations. |
| title | Well-posedness and Stability of Discrete Approximations for Controlled Sweeping Processes with Time Delay |
| topic | Optimization and Control 49J24, 49J25, 49J53, 49M25, 93B35 |
| url | https://arxiv.org/abs/2409.20404 |