Cyber-physical systems (CPSs), as emerging products of industry $4.0$, play a key role in the development of intelligent manufacturing. This paper proposes an observer-based adaptive neural network (NN) control for nonlinear strict-feedback CPSs subject to false data injection attacks. Since there may be strict constraints on the state or output signals of nonlinear cyber-physical systems (NCPSs), we propose a time-varying asymmetric barrier Lyapunov function to realize the specific output constraints of NCPSs under cyber-attacks. Besides, since false data injection attacks will corrupt the transmitted state variables, an observer is designed to obtain observations of the exact states, and NN is used to approximate the unknown nonlinearity of NCPSs. With the proposed control strategy, the constraint control problem of NCPSs subject to false data injection attacks is settled. Finally, a numerical simulation example verifies the effectiveness of the proposed controller.

This article is part of the theme issue ‘Towards symbiotic autonomous systems’.

信息物理系统 (CPS)，作为工业的新兴产品 $4.0$，在智能制造发展中发挥关键作用。本文针对受到虚假数据注入攻击的非线性严格反馈 CPS 提出了一种基于观察者的自适应神经网络 (NN) 控制。由于非线性网络物理系统（NCPS）的状态或输出信号可能存在​​严格的约束，我们提出了一个时变非对称势垒Lyapunov函数来实现网络攻击下NCPS的特定输出约束。此外，由于虚假数据注入攻击会破坏传输的状态变量，因此设计了一个观察器来获得对确切状态的观察，并且使用 NN 来近似 NCPS 的未知非线性。利用所提出的控制策略，解决了受到虚假数据注入攻击的NCPS的约束控制问题。最后，

这篇文章是主题问题“走向共生自治系统”的一部分。