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Invariant set-based analysis of minimal detectable fault for discrete-time LPV systems with bounded uncertainties

Abstract : This paper proposes an invariant-set based minimal detectable fault (MDF) computation method based on the set-separation condition between the healthy and faulty residual sets for discrete-time linear parameter varying (LPV) systems with bounded uncertainties. First, a novel invariant-set computation method for discrete-time LPV systems is developed exclusively based on a sequence of convex-set operations. Notably, this method does not need to satisfy the existence condition of a common quadratic Lyapunov function for all the vertices of the parametric uncertainty compared with the traditional invariant-set computation methods. Based on asymptotic stability assumptions, a family of robust positively invariant (RPI) outer-approximations of minimal robust positively invariant (mRPI) set are obtained by using a shrinking procedure. Based on the mRPI set, the healthy and faulty residual sets can be obtained. Then, by considering the dual case of the set-separation constraint regarding the healthy and faulty residual sets, we transform the guaranteed MDF problem based on the set-separation constraint into a simple linear programming (LP) problem to compute the magnitude of MDF. Since the proposed MDF computation method is robust regardless of the value of scheduling variables in a given convex set, fault detection (FD) can be guaranteed whenever the magnitude of fault is larger than that of the MDF. At the end of the paper, a practical vehicle model is used to illustrate the effectiveness of the proposed method. INDEX TERMS Invariant set, minimum detectable fault, LPV systems.
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Submitted on : Wednesday, October 30, 2019 - 1:10:52 AM
Last modification on : Friday, March 4, 2022 - 3:01:29 AM

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Junbo Tan, Sorin Olaru, Monica Roman, Feng Xu, Bin Liang. Invariant set-based analysis of minimal detectable fault for discrete-time LPV systems with bounded uncertainties. IEEE Access, IEEE, 2019, 7, pp.152564-152575. ⟨10.1109/ACCESS.2019.2948362⟩. ⟨hal-02338407⟩

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