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

Junbo Tan (1, 2) , Sorin Olaru (2) , Monica Roman (3) , Feng Xu (1) , Bin Liang (1)

1 THU - Tsinghua University [Beijing]
2 L2S - Laboratoire des signaux et systèmes
3 University of Craiova

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.

Domaines: Automatique / Robotique

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, 2019, 7, pp.152564-152575. ⟨10.1109/ACCESS.2019.2948362⟩. ⟨hal-02338407⟩