SIAM Journal on Control and Optimization, Volume 58, Issue 6, Page 3613-3631, January 2020.
We study an optimal control problem governed by a class of Pyragas-type nonlocal feedback controllers with time-delay for the convective FitzHugh--Nagumo equation. An optimal control problem is constrained by a coupled nonlinear system of parabolic partial differential equations. Well-posedness of the feedback control system and the differentiability of the control-to-state mapping are proved. Further, the main goal of the paper is to establish existence results for the distributed optimal kernels in the controllers. In particular, we take kernels as control functions, and we show that optimal kernels are the solution to the optimal control problem. Furthermore, we also derive the first-order necessary optimality conditions.

中文翻译：

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对流时滞FitzHugh-Nagumo方程的非局部Pyragas反馈控制器的最优控制问题

SIAM控制与优化杂志，第58卷，第6期，第3613-3631页，2020年1月。
我们研究对流FitzHugh-Nagumo方程的一类具有时滞的Pyragas型非局部反馈控制器控制的最优控制问题。 。最优控制问题受到抛物线偏微分方程的耦合非线性系统的约束。证明了反馈控制系统的适定性和控制状态映射的可微性。此外，本文的主要目标是建立控制器中分布式最优核的存在性结果。特别地，我们将核作为控制函数，并且证明了最优核是最优控制问题的解决方案。此外，我们还推导了一阶必要最优性条件。