Gain-Scheduled Fault Detection Filter for Discrete-Time LPV Systems

Abstract

The present work investigates a fault detection problem using a gain-scheduled filter for discrete-time Linear Parameter Varying systems. We assume that the scheduling parameter cannot be directly measured but, instead, it is estimated. On the one hand, this assumption imposes the challenge that the fault detection filter should perform properly even when using an inexact parameter but, on the other, it avoids the burden associated with the design of a complex estimation process for this parameter. Three design approaches are proposed, namely, the H 2 , H ∞ , and mixed H 2 / H ∞ gain-scheduled Fault Detection Filters which are designed via Linear Matrix Inequalities. We also provide numerical simulations to illustrate the applicability and performance of the proposed novel methods.INDEX TERMS Fault Detection and Isolation, LPV systems, H 2 gain-scheduled filter, H ∞ gain-scheduled filter

Improved robust filter synthesis combining linear matrix inequalities and heuristic algorithms

“…Filtering problems usually involve uncertainties and additional performance indexes, such as the $$$ {\mathscr{H}}_2 $$$ and $$$ {\mathscr{H}}_{\infty } $$$ norms. Recent works exploring $$$ {\mathscr{H}}_2 $$$ and $$$ {\mathscr{H}}_{\infty } $$$ guaranteed costs for filtering and fault detection can be mentioned, 7‐10 as well as control problems 11‐13 . The solution of $$$ {\mathscr{H}}_2 $$$ and $$$ {\mathscr{H}}_{\infty } $$$ problems are often initially modeled as a set of bilinear matrix inequalities (BMIs), which are NP‐hard and, thus, difficult to solve 14 .…”