In this paper, the trajectory tracking control and the field programmable gate array (FPGA) implementation between a recurrent neural network with time delay and a chaotic system are presented. The tracking error is globally asymptotically stabilized by means of a control law generated from the Lyapunov–Krasovskii and Lur’e theory. The applicability of the approach is illustrated by considering two different chaotic systems: Liu chaotic system and Genesio–Tesi chaotic system. The numerical results have shown the effectiveness of obtained theoretical results. Finally, the theoretical results are implemented on an FPGA, confirming the feasibility of the synchronization scheme and showing that it is hardware realizable.

中文翻译：

---

涉及混沌系统和时延神经网络的主从同步方案的 FPGA 实现和 Lyapunov-Krasovskii 分析

在本文中，提出了具有时延的递归神经网络和混沌系统之间的轨迹跟踪控制和现场可编程门阵列（FPGA）实现。跟踪误差通过 Lyapunov-Krasovskii 和 Lur'e 理论生成的控制律在全局渐近稳定。通过考虑两个不同的混沌系统来说明该方法的适用性：Liu 混沌系统和 Genesio-Tesi 混沌系统。数值结果表明了所得理论结果的有效性。最后，理论结果在FPGA上实现，证实了同步方案的可行性，并表明它是硬件可实现的。