Funnel adaptive neural learning secure control for nonlinear cyber-physical systems under stochastic FDI attacks

This paper discusses the funnel adaptive neural learning secure control for nonlinear cyber-physical systems with stochastic false data injection attacks. A new defense strategy based on reinforcement learning with an identifier-critic-actor structure is proposed. This strategy not only effectively estimate unknown dynamics, evaluate system performance, and execute control actions, but also improves the robustness of the controlled system, and ensures that the tracking errors converge within the funnel in the finite-time. The control scheme aims to design the actual control inputs for all virtual controls and dynamic surface controls as the optimal solution of the corresponding subsystems. The update law is derived using the negative gradient of a simple positive function, which is generated from the partial derivatives of the Hamilton-Jacobi-Bellman equation. In addition, the Nussbaum function is introduced to compensate for the negative impact of the unknown direction of false data injection attacks on the sensors. At the same time, the design can also alleviate the requirements of the current optimal control methods for continuous excitation conditions. A key innovation lies in the formulation of elastic functions with flexible capabilities, thereby providing a unified framework that can flexibly solve the situation of initial value constraints without changing the control structure. Stability analysis shows that all signals are probabilistically semi-globally uniformly ultimately bounded.