Reliability-Guaranteed Fault Observer Design for Systems With Stochastic Parametric Uncertainty

Abstract

The existing observer-based fault estimation methods for dynamic systems rarely consider the internal stochastic parametric uncertainty, limiting the reliability in practical applications. This letter aims to design a reliability-guaranteed fault observer for systems with stochastic parametric uncertainty. The condition for the observer stability and performance robustness is first described by a stochastic linear matrix inequality (LMI). By introducing the structural reliability index and certain matrix inequality lemmas, the original stochastic LMI is transformed into a deterministic probabilistic LMI with a probabilistic parameter of the reliability index. The probabilistic parameter quantifies the likelihood of achieving fault estimation performance and can be intentionally given or optimized to design a reliable fault observer. Simulation results with Monte-Carlo verification demonstrate the capability of the designed fault observer to estimate the constant and slowly time-varying faults, outperforming conventional methods in reliability.