Cyber-Resilient Covariance Control of Interval Type-2 Fuzzy Stochastic Nonlinear Systems with D-Stable Transient Regulation

Abstract

: An Interval Type-2 (IT2) Fuzzy Controller (FC) design approach and a Linear Matrix Inequality (LMI)- based computational analysis method are proposed in this paper for Uncertain Stochastic Nonlinear Systems (USNSs) subject to deception attacks. For USNSs, the IT2 Takagi-Sugeno Fuzzy Model (TSFM) is constructed to characterize uncertainty effects more completely through lower and upper Membership Functions (MFs). Based on these MFs, the corresponding IT2 FC is also developed. For the closed-loop IT2 TSFM, covariance control theory is integrated with IT2 fuzzy control to suppress the state energy induced by stochastic behaviors from the steady-state perspective. In addition, the variance constraint is introduced to restrict the individual state responses below prescribed bounds. Different from existing studies, the passivity performance constraint over the whole-time interval is further integrated to attenuate stochastic behaviors regarded as external disturbance inputs. To address transient response requirements, the D -Stable Pole Placement (DSPP) method is also introduced to constrain the closed-loop poles of the dominant terms in IT2 TSFM within a prescribed disk region. This integrated framework simultaneously addresses uncertainties, stochastic state-energy suppression, disturbance attenuation, and transient-response regulation under deception attacks. Then, LMI-based stability and performance conditions are derived using the upper-bound matrix technique, such that the IT2 FC design problem can be solved through a convex optimization computational analysis process. Finally, the proposed IT2 FC design approach is applied to a ship rolling motion system modeled as a USNS, with comparative simulation results demonstrating the effectiveness and advantages.