In this paper we consider a class of feedback control systems described by an evolution hemivariational inequality involving history-dependent operators. Under the mild conditions, first, we prove a priori estimates of the solutions to the feedback control system. Then, an existence theorem for the feedback control system is obtained by using the well-known Bohnenblust-Karlin fixed point theorem. Moreover, we consider an optimal control problem driven by the feedback control system, and establish its solvability. Finally, a parabolic partial differential system with Clarke subgradient term is considered to illustrate the applicability of the theoretical results.

在本文中，我们考虑一类由涉及历史相关算子的演化半变分不等式描述的反馈控制系统。在温和的条件下，首先，我们证明了反馈控制系统解决方案的先验估计。然后，通过使用众所周知的 Bohnenblust-Karlin 不动点定理，获得反馈控制系统的存在定理。此外，我们考虑了一个由反馈控制系统驱动的最优控制问题，并建立了它的可解性。最后，考虑了一个具有克拉克次梯度项的抛物线偏微分系统来说明理论结果的适用性。