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.

This paper investigates the adaptive fuzzy sliding exact tracking control problem of a class of high-order nonlinear systems with full-state constraints and mismatched external disturbances. To achieve exact tracking control, the upper bound of a composite polynomial is estimated, which is composed of approximation error, mismatched disturbance and virtual control law and its upper bound estimated information is employed in the controller design. In this way, once the tracking error deviates from the origin, the corresponding adaptive fuzzy sliding exact tracking control mechanism will be activated to force it to slide along the origin, and then exact tracking control is achieved. Meanwhile, high-order log-type time-varying barrier Lyapunov functions (TVBLFs) are introduced to ensure that the full-state constraint is not violated. A 2-D high-order nonlinear systems and an underactuated nonlinear benchmark system with weak coupling are considered to illustrate the characteristics of the control mechanism in Simulation.

This paper investigates the adaptive sliding mode security control (ASMSC) problem of rotary inverted pendulum against randomly occurring false data injection attacks (ROFDIAs). To accomplish the control objectives for both swing-up and stabilization stages, this study proposes an adaptive backstepping nonlinear control method and an ASMSC method, respectively. These approaches distinctly differ from conventional strategies such as energy-based swing-up control methods, linear quadratic regulators, or adaptive sliding mode control techniques. Besides, note that the existing control methods are proposed in the normal network environment, once the network is malicious attacks, these methods will be invalid. Based on this, a novel ASMSC method is proposed of rotating inverted pendulum against ROFDIAs. Meanwhile, the validity of the proposed method is proved by two comparative experiments on the hardware-in-the-loop simulation platform.