A health performance prediction method of large-scale stochastic linear hybrid systems with small failure probability

Abstract

Health performance prediction of a dynamical system aims at determining the probability or possibility that the system state will remain in a permitted area (safe set) or reach a forbidden area (unsafe set) at a future time instance. This paper proposes a health performance prediction algorithm for large-scale Stochastic Linear Hybrid Systems (SLHS) with small failure probability. In the studied SLHS, the continuous variable evolution is described by a set of stochastic linear differential equations, and the discrete state evolution is modeled by a first-order Markov chain. Furthermore, a safe set of the SLHS is described by a permitted area in the hybrid state space. Given an initial condition, a hybrid state evolution algorithm is proposed referring to the execution of stochastic hybrid systems. On this basis, a concept of health degree is introduced to evaluate the health performance of the studied SLHS. Finally, a multicopter with sensor anomalies is studied to validate the availability and effectiveness of the proposed method.