Observer-Based Fuzzy Fault-Tolerant Control for Nonlinear Systems in the Presence of General Noise

Ximing Yang

Abstract: This paper addresses the observer-based fuzzy fault-tolerant control problem for nonlinear systems subject to general noise. The presence of component faults and general noise can significantly alter system behavior, potentially leading to instability. Stochastic differential equations theory is an effective tool for managing control problems in interval type-2 T-S fuzzy systems influenced by white noise. However, compared to stochastic differential equations, random differential equations are more suitable when random disturbances are better described by stationary processes rather than white noise. In this paper, the problem of observer-based fault-tolerant control for nonlinear systems with general noise is solved using a mixed design method that combines an interval type-1 observer with an interval type-2 controller. Furthermore, by describing the effects of stationary processes on the system using general noise and applying random differential equation theory, the probabilistic stabilization of the system is analyzed, and LMIs-based stability criteria are derived in the observer design process. Similar results are also obtained in the controller design process. The proposed method not only reduces the computational burden of designing fault-tolerant controllers in the presence of general noise but also provides results with lower conservatism, allowing for greater uncertainty handling. Finally, the effectiveness of the proposed method is demonstrated through an example.

Submission Number: 205