Security Interval Type-2 Fuzzy Sliding Mode Control Under Multi-Strategy Injection Attack: Design, Analysis, and Optimization

In this work, the security sliding mode control problem is considered for interval type-2 (IT2) fuzzy systems, where the sensor-controller channel may be subject to the false data injection attack with multi-strategy attack model. The different attack patterns at each instant is described via a random categorical distribution. It is noted that the injected false data may result in the system state to exceed the modeling domain. In order to cope with the above phenomenon, a reconstruction method of the controller's membership functions is proposed via analyzing the variation range of the attacked state, and then, an IT2 fuzzy sliding mode controller is designed. The explicit relation between the raw state signal and attacked state is established, based on which stability conditions dependent on the regional boundaries of membership functions are obtained for the input-to-state stability in probability of the closed-loop system. Meanwhile, a framework of security performance optimization is established via searching a desirable sliding matrix, which may be solved via the particle swarm optimization algorithm. Furthermore, the proposed security control scheme is extended to the case of imperfectly matched premises, where the controller may have different fuzzy rules from the fuzzy system. Finally, the proposed security control scheme is verified by two simulations examples.