带负折扣的无限时域最优控制渐近稳定控制问题
Asymptotically stable control problems by infinite horizon optimal control with negative discounting
摘要：
对于既有吸引子又有稳定不动点的系统，本文首先提出了新的稳定控制问题，找到了渐近稳定的控制函数，实现了将围绕吸引子运动的状态转移到稳定的不动点。然后利用基于负折扣的无限时域最优控制模型的常微分方程，给出了二维情形下稳定控制问题的一个解答。在一定条件下，证明了相空间可以分离为若干开连通分支，这取决于分支中从初始点开始的轨道的渐近性态。这种对初始点的分类表明能够鲁棒地实现稳定控制。此外，我们说明了一些数值结果的稳定控制所获得的应用我们的聚焦系统的Bonhoven-van der Pol模型。
英文摘要：
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.
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