LAUSR

In this article, the main contribution is to introduce the adaptive backstepping technique into nonlinear cyber–physical systems against randomly occurring false data injection (ROFDI) attacks. And a new defense strategy based on nonlinear disturbance observer (NDO) is developed, which can not only effectively estimate the external compound disturbance in the presence of the attack, but also improve the robustness of the controlled system. Different from FDI attacks, it is a special case of ROFDI attacks, and the proposed method can deal with ROFDI attacks injected by attackers. Meanwhile, multiple Nussbaum functions are introduced, which overcomes the design difficulty of unknown control directions caused by ROFDI attacks. Furthermore, the approximation of the unknown nonlinear function and the exponential growth problem in the traditional backstepping calculation process are handled by radial basis function neural network and dynamic surface control, respectively. Finally, a new adaptive neural control method based on NDO is proposed to make all signals bounded. Meanwhile, tracking errors and disturbance estimation errors converge on the neighborhood of zero. Numerical and practical examples further illustrate the rationality of the method.