In this article, the novel adaptive neural networks (NNs) tracking control scheme is presented for nonlinear partial differential equation (PDE)-ordinary differential equation (ODE) coupled systems subject to deception attacks. Because of the special infinite-dimensional characteristics of PDE subsystem and the strong coupling of PDE-ODE systems, it is more difficult to achieve the tracking control for coupled systems than single ODE system under the circumstance of deception attacks, which result in the states and outputs of both PDE and ODE subsystems unavailable by injecting false information into sensors and actuators. For efficient design of the controllers to realize the tracking performance, a new coordinate transformation is developed under the backstepping method, and the PDE subsystem is transformed into a new form. In addition, the effect of the unknown control gains and the uncertain nonlinearities caused by attacks are alleviated by introducing the Nussbaum technology and NNs. The proposed tracking control scheme can guarantee that all signals in the coupled systems are bounded and the good tracking performance can be achieved, despite both sensors and actuators of the studied systems suffering from attacks. Finally, a simulation example is given to verify the effectiveness of the proposed control method.

中文翻译：

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基于 Nussbaum 的自适应神经网络对受欺骗攻击的非线性 PDE-ODE 系统的跟踪控制


本文针对遭受欺骗攻击的非线性偏微分方程 （PDE）-常微分方程 （ODE） 耦合系统，提出了一种新的自适应神经网络 （NN） 跟踪控制方案。由于偏微分方程子系统的特殊无限维特性和偏微分方程-常微分方程系统的强耦合性，在欺骗攻击的情况下，比单个常微分方程系统更难实现对耦合系统的跟踪控制，导致偏微分方程和常微分方程子系统的状态和输出都无法通过向传感器和执行器注入虚假信息而不可用。为了实现跟踪性能的高效设计，该文在反步方法下开发了一种新的坐标变换方法，并将偏微分方程子系统转化为一种新的形式。此外，通过引入 Nussbaum 技术和 NNs，可以减轻未知控制增益和攻击引起的不确定非线性的影响。所提出的跟踪控制方案可以保证耦合系统中的所有信号都是有界的，并且可以获得良好的跟踪性能，尽管所研究系统的传感器和执行器都受到攻击。最后，通过仿真算例验证了所提控制方法的有效性。