论文标题
库拉莫托 - 西瓦辛斯基方程的强大stackelberg可控性
Robust Stackelberg Controllability for the Kuramoto-Sivashinsky Equation
论文作者
论文摘要
在本文中，研究了非线性四阶抛物线方程（即库拉莫托 - sivashinsky方程）的鲁棒stackelberg可控性（RSC）问题。当三个外部来源作用到系统中时，RSC问题基本上是结合两个子问题：第一个是两个来源之间的鞍点问题。这样的来源称为“追随者控制”及其相关的“干扰信号”。此过程对应于强大的控制问题。第二个是层次控制问题（Stackelberg策略），其中涉及第三力量，所谓的领导者控制。 RSC问题为这些力量建立了同时的游戏，从某种意义上说，领导者的控制具有验证可控性属性的客观，而追随者控制和扰动解决了强大的控制问题。在本文中，领导者控制了对轨迹的确切可控性。此外，开发和实施了近似稳健控制问题的迭代算法以及非线性kuramoto-sivashinsky方程的鲁棒stackelberg策略。
In this article the robust Stackelberg controllability (RSC) problem is studied for a nonlinear fourth-order parabolic equation, namely, the Kuramoto-Sivashinsky equation. When three external sources are acting into the system, the RSC problem consists essentially in combining two subproblems: the first one is a saddle point problem among two sources. Such an sources are called the "follower control" and its associated "disturbance signal". This procedure corresponds to a robust control problem. The second one is a hierarchic control problem (Stackelberg strategy), which involves the third force, so-called leader control. The RSC problem establishes a simultaneous game for these forces in the sense that, the leader control has as objective to verify a controllability property, while the follower control and perturbation solve a robust control problem. In this paper the leader control obeys to the exact controllability to the trajectories. Additionally, iterative algorithms to approximate the robust control problem as well as the robust Stackelberg strategy for the nonlinear Kuramoto-Sivashinsky equation are developed and implemented.
