Globally Finite time and Globally Fixed-time stable Dynamical Systems for solving Inverse Quasi-variational inequality problems
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909528014979072 |
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| author | Van Tran, Nam Hai, Le Thi Thanh |
| author_facet | Van Tran, Nam Hai, Le Thi Thanh |
| contents | In this paper, we propose two projection dynamical systems for solving inverse quasi-variational inequality problems in finite-dimensional Hilbert spaces-one ensuring finite-time stability and the other guaranteeing fixed-time stability. We first establish the connection between these dynamical systems and the solutions of inverse quasi-variational problems. Then, under mild conditions on the operators and parameters, we analyze the global finite-time and global fixed-time stability of the proposed systems. Both approaches offer accelerated convergence, however, while the settling time of a finite-time stable dynamical system depends on initial conditions, the fixed-time stable system achieves convergence within a predefined time, independent of initial conditions. To demonstrate their effectiveness, we provide numerical experiments, including an application to the traffic assignment problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Globally Finite time and Globally Fixed-time stable Dynamical Systems for solving Inverse Quasi-variational inequality problems Van Tran, Nam Hai, Le Thi Thanh Optimization and Control 47J20, 47J30, 49J40, 49J53, 49M37 In this paper, we propose two projection dynamical systems for solving inverse quasi-variational inequality problems in finite-dimensional Hilbert spaces-one ensuring finite-time stability and the other guaranteeing fixed-time stability. We first establish the connection between these dynamical systems and the solutions of inverse quasi-variational problems. Then, under mild conditions on the operators and parameters, we analyze the global finite-time and global fixed-time stability of the proposed systems. Both approaches offer accelerated convergence, however, while the settling time of a finite-time stable dynamical system depends on initial conditions, the fixed-time stable system achieves convergence within a predefined time, independent of initial conditions. To demonstrate their effectiveness, we provide numerical experiments, including an application to the traffic assignment problem. |
| title | Globally Finite time and Globally Fixed-time stable Dynamical Systems for solving Inverse Quasi-variational inequality problems |
| topic | Optimization and Control 47J20, 47J30, 49J40, 49J53, 49M37 |
| url | https://arxiv.org/abs/2503.04590 |