Input-to-State Stabilization of Interval Type-2 Fuzzy Systems Subject to Cyberattacks: An Observer-Based Adaptive Sliding Mode Approach

Abstract

This paper focuses on the sliding mode control (SMC) problem of interval type-2 (IT2) fuzzy systems subject to the unmeasurable state and cyberattacks. A key issue is how to design a state observer under the constraint that only the bounds of membership functions are known. To this end, this paper introduces two weighting factors to construct a new membership function. Besides, the concept of input-to-state stability (ISS) is utilized to deal with the residual term resulting from the cyberattacks and external disturbances. The sufficient condition is established such that the sliding mode dynamics and the estimated error dynamics are input-to-state stable. Furthermore, by online estimating the unknown parameters in upper bounds of cyberattacks and external disturbances, an adaptive sliding mode controller is synthesized such that the reachability of the prescribed sliding surface can be guaranteed and the effect of cyberattacks on the system performance can be effectively attenuated. Finally, the validity of the proposed method is illustrated by a mass–spring–damper system.