论文标题
通过无限的地平线最佳控制和负折扣，渐近稳定的控制问题
Asymptotically stable control problems by infinite horizon optimal control with negative discounting
论文作者
论文摘要
在本文中，对于具有吸引子和稳定固定点的系统，我们首先提出新的稳定控制问题，以找到渐近稳定的控制函数，该功能意识到可以将一个状态转移到吸引子上的状态到稳定的固定点。然后，通过基于带有负折扣的无限视野最佳控制模型的普通微分方程，我们在二维情况下为稳定控制问题提供了一个答案。此外，在某些条件下，我们验证了相位空间可以根据从其组件中的初始点开始的轨道的渐近行为分离到某些开放的连接组件。初始点的这种分类表明，它可以鲁棒地实现稳定的控制。此外，我们说明了通过将重点系统应用于Bonhoeffer-Van der Pol模型获得的稳定控制的一些数值结果。
In the paper, for the system which possesses both an attractor and a stable fixed point, we first formulate new stable control problems to find the asymptotically stable control function which realizes to transit a state moving around the attractor to the stable fixed point. Then by using the ordinary differential equation based on the infinite horizon optimal control model with negative discounts, we give one of answers for the stable control problem in a two-dimensional case. Furthermore, under some conditions, we verify that the phase space can be separated to some open connected components depending on the asymptotic behavior of the orbit starting from the initial point in their components. This classification of initial points suggests that it is enable to robustly achieve a stable control. Moreover, we illustrate some numerical results for the stable control obtained by applying our focused system for the Bonhoeffer-van der Pol model.
