Calculation of Critical Fault Recovery Time for Nonlinear Systems Based on Region of Attraction Analysis

Abstract

In safety critical systems, the control system is composed of a core control system with a fault detection and isolation scheme together with a repair or a recovery strategy. The time that it takes to detect, isolate, and recover from the fault (fault recovery time) is a critical factor in safety of a system. It must be guaranteed that the trajectory of a system subject to fault remains in the region of attraction (ROA) of the post-fault system during this time. This paper proposes a new algorithm to compute the critical fault recovery time for nonlinear systems with polynomial vector fields using sum of squares programming. The proposed algorithm is based on computation of ROA of the recovered system and finite-time stability of the faulty system.