1-Order-Smooth Explicit-Time Nonsingular Terminal Sliding Mode Control of Industrial Cyber-Physical Systems Against Cyber-Attacks

In the existing terminal sliding mode tracking controller design of the industrial cyber-physical systems (ICPSs) against cyber-attacks, the convergence time and tracking precision can not be predefined simultaneously due to singular problem. To solve this problem, for ICPSs under randomly occurring injection attacks, this paper presented a novel explicit-time nonsingular terminal sliding mode control (TSMC) method. Firstly, a novel 1-order-smooth symmetric system structure was found to construct an explicit-time stable system. It was 1-order-smooth at the steady-state boundary. Then, the singularity of the explicit-time terminal sliding mode nominal controller was analyzed from three aspects: narrow sense, broad sense and practical sense. Finally, based on above analysis, a novel 2-order nonsingular explicit-time TSMC method for ICPSs was proposed without the cost of convergence time and precision. Compared with other related methods, this method had more controllable convergence performance and smoother control input. Theoretical results were verified by simulation and experiment.