A Hierarchical Robust Control Strategy for Stochastic Kuramoto--Sivashinsky--Korteweg--de Vries Equations
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917401600196608 |
|---|---|
| author | Elgrou, Abdellatif Oukdach, Omar Rhandi, Abdelaziz |
| author_facet | Elgrou, Abdellatif Oukdach, Omar Rhandi, Abdelaziz |
| contents | We investigate the robust Stackelberg null controllability of a one-dimensional forward linear stochastic Kuramoto--Sivashinsky--Korteweg--de Vries (KS--KdV) equation. The control framework is formulated as a hierarchical Stackelberg game involving two leaders, one follower, and worst-case disturbances acting in both the drift and diffusion terms. The first leader acts to drive the system to rest, while the second leader is introduced to overcome analytical difficulties arising from the stochastic setting. The follower, by reducing the effect of the disturbances, addresses a tracking-type control problem aimed at keeping the system state and its first and second spatial derivatives close to prescribed target trajectories. First, the robust control problem is characterized by the existence of a saddle point. Then, the analysis is reduced to the null controllability of a strongly coupled forward--backward stochastic KS--KdV system. The problem is addressed by combining a duality technique with new Carleman estimates for forward and backward stochastic fourth-order parabolic equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10714 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Hierarchical Robust Control Strategy for Stochastic Kuramoto--Sivashinsky--Korteweg--de Vries Equations Elgrou, Abdellatif Oukdach, Omar Rhandi, Abdelaziz Optimization and Control We investigate the robust Stackelberg null controllability of a one-dimensional forward linear stochastic Kuramoto--Sivashinsky--Korteweg--de Vries (KS--KdV) equation. The control framework is formulated as a hierarchical Stackelberg game involving two leaders, one follower, and worst-case disturbances acting in both the drift and diffusion terms. The first leader acts to drive the system to rest, while the second leader is introduced to overcome analytical difficulties arising from the stochastic setting. The follower, by reducing the effect of the disturbances, addresses a tracking-type control problem aimed at keeping the system state and its first and second spatial derivatives close to prescribed target trajectories. First, the robust control problem is characterized by the existence of a saddle point. Then, the analysis is reduced to the null controllability of a strongly coupled forward--backward stochastic KS--KdV system. The problem is addressed by combining a duality technique with new Carleman estimates for forward and backward stochastic fourth-order parabolic equations. |
| title | A Hierarchical Robust Control Strategy for Stochastic Kuramoto--Sivashinsky--Korteweg--de Vries Equations |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.10714 |