Adaptive Neural Sliding Mode Control-Based Real-Time Security Reachable Set Control of Markov Jump Cyber–Physical Systems Against Actuator Attacks

This article addresses the real-time security reachable set (RS) control problem for nonlinear semi-Markov jump cyber–physical systems (s-MJCPSs) subject to multiple time-varying delays and actuator attacks. Then, based on the neural network (NN) approximation approach and employing a sliding mode control (SMC) strategy, an adaptive NN SMC scheme is proposed to tackle challenges arising from nonlinear attack functions and mode jumps. The proposed strategy ensures s-MJCPSs stability and mean-square boundedness of system states within a predefined RS. Sufficient conditions for real-time security RS control are derived. Finally, an example is presented to demonstrate the effectiveness of the proposed strategy in realizing adaptive real-time RS control.