Invariant set-based robust fault detection and optimal fault estimation for discrete-time LPV systems with bounded uncertainties. Issue 16 (10th December 2019)

• Record Type: Journal Article
• Authors: Tan, Junbo; Xu, Feng; Wang, Xueqian; Yang, Jun; Liang, Bin
• Is Part Of: International journal of systems science. Volume 50:Issue 16(2019)
• Page Start: 2962
• Page End: 2978
• Publication Date: 2019-12-10
• Subjects: Fault detection -- fault estimation -- invariant set -- zonotopic Kalman filter -- discrete-time LPV systems; System analysis -- Periodicals; 003.3
• DOI: 10.1080/00207721.2019.1691283
• Languages: English
• ISSNs: 0020-7721

Abstract

ABSTRACT: This paper proposes an invariant set-based robust fault detection (FD) and optimal fault estimation (FE) method for discrete-time linear parameter varying (LPV) systems with bounded uncertainties. Firstly, a novel invariant-set construction method for discrete-time LPV systems is proposed if and only if the system is poly-quadratically stable, which need not satisfy the condition that there must exist a common quadratic Lyapunov function for all vertex matrices of the system compared to the traditional invariant-set construction methods. Furthermore, by using a shrinking procedure, we provide minimal robust positively invariant (mRPI) set approximations that are always positively invariant at each step of iteration and allow a priori desired precision to obtain a high sensitivity of FD. Owing to the existence of invariant set-based FD phase, the assumption that the initial faults should be bounded by a given set can be avoided for FE. We compute an optimal parametric matrix gain by minimising the Frobenius norm-based size of the corresponding FE set to obtain the optimal FE performance. Theoretically, any trajectory in the FE tube can be chosen as a specific-value estimation for the real fault signals. Finally, a vehicle dynamics system is used to illustrate the effectiveness of the proposed method.