A RISK ADJUSTED APPROACH TO ROBUST SIMULTANEOUS FAULT DETECTION AND ISOLATION Mario Sznaier ∗ Wenjing Ma ∗ Constantino Lagoa ∗ ∗ Department of Electrical Engineering The Pennsylvania State University University Park, PA 16802 Abstract: In this paper we address the problem of detecting and isolating faults from noisy input/output measurements of a MIMO uncertain–system, subject to structured dynamic uncertainty. The main result of the paper shows that this problem can be solved in a computationally efficient way by using a combination of sampling and LMI optimization tools. These results are illustrated using a simplified model of a flight control system. Copyright c  2005 IFAC Keywords: Fault Detection, Fault Isolation, Model (In)Validation 1. INTRODUCTION The problem of Fault Detection and Isolation (FDI) in control systems has been the subject of considerable attention during the past two decades. This research has resulted in a variety of methods and a vast amount of papers in the literature (see for instance (Frank and Ding 1997, Gertler 1998, Patton 1994) and ref- erences therein). Many of these methods are based on a model–based approach, also known as analytical or functional redundancy. In contrast to approaches based on physical or hardware redundancy, the former exploit the mathematical model of the system under consideration, leading to a two stage procedure: (i) residual generation and, (ii) decision making. While appealing, since it does not require additional hardware, a potential problem with the analytical ap- proach is its fragility: a mismatch between the ac- tual plant and the model used in the FDI algorithm can result in false alarms. To avoid this difficulty, the algorithm must be robust both against modelling er- rors and exogenous disturbances. Robust FDI methods have been well studied (see for instance (Collins and Song 2000, Emaimi-Naeimi et al. 1998, Frank and Ding 1997, Henry et al. 2001, Jiang et al. 2002, Patton 1994, Saberi et al. 2000, Stoustrup and Niemann 2003, Zhong et al. 2003) and references therein). A potential disadvantage of these methods is the difficulty in iso- lating the exact location of the fault and in detecting simultaneous faults. Moreover, in the case of dynamic uncertainty, this problem is generically non–convex in all variables involved(Shim and Sznaier 2003) and thus computationally hard to solve. In this paper we propose to solve these difficulties by pursuing a risk–adjusted approach, based on sam- pling the uncertainty set. This removes one of the interpolation constraints that renders the problem non- convex, allowing for efficient solutions. The proposed new FDI framework has the following advantages over currently existing methods: (a) It allows for handling arbitrary dynamic uncer- tainty structures (as opposed to parametric uncer- tainty) (b) It allows for arbitrary fault dynamics, rather than having the fault and nominal operation sharing the same dynamic matrix A. In addition, it also provides an estimate of which fault has occurred. (c) Its computational complexity grows only poly- nomially with the dimension of the plant.