Theoretical analysis and control results for the Fitzhugh-Nagumo equation
Theoretical analysis and control results for the Fitzhugh-Nagumo equation
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发表时间：
2008
影响因子：
0.7
通讯作者：
Adilson J. V. Brandão;E. Fernández-Cara;P. M. D. Magalhães;M. Rojas-Medar
中科院分区：
文献类型：
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作者：
Adilson J. V. Brandão;E. Fernández-Cara;P. M. D. Magalhães;M. Rojas-Medar
本文讨论了Fitzhugh-Nagumo方程的一些理论问题。首先，我们回顾了系统，简单地解释了变量的含义，并给出了强解的存在唯一性的简单证明。我们还考虑了该系统的最优控制问题。在这种情况下，我们的目标是确定我们如何对系统采取行动，以获得良好的属性。我们证明了最优状态控制对的存在性，并且作为Dubovitski-Milyoutin形式的应用，我们推导了相应的最优性系统。我们还将最优控制问题与可控性问题联系起来，并构造了一系列控制，这些控制产生强收敛于期望状态的解。这提供了一种使系统按所需方式运行的策略。最后，我们提出了一些与该方程的控制有关的问题。
In this paper we are concerned with some theoretical questions for the FitzHugh-Nagumo equation. First, we recall the system, we briefly explain the meaning of the variables and we present a simple proof of the existence and uniqueness of strong solution. We also consider an optimal control problem for this system. In this context, the goal is to determine how can we act on the system in order to get good properties. We prove the existence of optimal state-control pairs and, as an application of the Dubovitski-Milyoutin formalism, we deduce the corresponding optimality system. We also connect the optimal control problem with a controllability question and we construct a sequence of controls that produce solutions that converge strongly to desired states. This provides a strategy to make the system behave as desired. Finally, we present some open questions related to the control of this equation.