A geometric approach to fault detection and isolation for bilinear systems

Algebraic approach for model decomposition: Application to fault detection and isolation in discrete-event systems

“…Time-driven model-based FDI is achieved by analysing fault indicators or residuals, which are signals obtained by comparing measured outputs of the monitored process with the corresponding simulated outputs. Three major techniques are used for residual generation (Patton, 1994;Isermann, 2005): the parameter estimation approach (Isermann, 1984;Isermann and Freyermuth, 1991) or, more recently (Fliess and Join, 2003;Fliess et al, 2004), the parity space approach (Gertler, 1991;Staroswiecki and Comtet-Varga, 2001) based on elimination (Diop, 1991;Cox et al, 1991;Staroswiecki and Comtet-Varga, 2001) or on projection (Chow and Willsky, 1984;Isidori, 1995;Leuschen et al, 2005), and the observer-based approach (Patton, 1994;Hammouri et al, 2001;Jiang et al, 2004;2006;Lootsma, 2001).…”

A graph-theoretic approach to fault detection and isolation for structured bilinear systems

“…The BFPRG has been treated and solved in (Hammouri et al 2001) for non structured systems using a geometric approach. By a straightforward extension of the results enounced in (Hammouri et al 2001) to SBLS, we can deduce that, in the single fault case (q = 1), the BFPRG has generically a solution iff for almost all the realizations of system (1), E Ō H , whereŌ H is the minimal unobservability subspace containing Im(H).…”

“…In (Kinnaert 1999), the author proposes two robust FDI schemes for BLS which are not necessarily affine in the failure modes. Finally, one of the most important results is given in (Hammouri et al 2001). Using a geometric approach, the authors provide necessary and sufficient conditions for the solvability of the so-called bilinear fundamental problem of residual generation (BFPRG).…”

An LMI approach to robust fault estimation for a class of nonlinear systems

“…One of the standard methods for observer design, which can be applied for fault diagnosis and FTC, consists in using the non-linear change of coordinates to bring the original system into a linear one (a pseudo linear one) [16,20]. It is worth noting that there are efficient approaches for bilinear systems [15]. It should be also pointed out that, when the feasibility condition of the above schemes are not matched, then the well known Extended Kalman Filter (EKF) can be applied in both a stochastic and a deterministic context (see, e.g., [47]).…”