Nussbaum-Based Adaptive Neural Networks Tracking Control for Nonlinear PDE-ODE Systems Subject to Deception Attacks
针对遭受欺骗攻击的非线性偏微分方程-常微分方程耦合系统，提出了一种基于Nussbaum技术和自适应神经网络的跟踪控制方案，通过坐标变换和神经网络处理未知增益与不确定性，保证系统信号有界并实现良好跟踪性能。
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.