Robust Fault Diagnosis for a Satellite System Using a Neural Sliding Mode Observer Qing Wu and Mehrdad Saif Abstract— In this paper a nonlinear observer which synthe- sizes sliding mode techniques and neural state space models is proposed and is applied for robust fault diagnosis in a class of nonlinear systems. The sliding mode term is utilized to eliminate the effect of system uncertainties, and the switching gain is updated via an iterative learning algorithm. Moreover, the neural state space models are adopted to estimate state faults. Theoretically, the robustness, sensitivity, and stability of this neural sliding mode observer-based fault diagnosis scheme are rigorously investigated. Finally, the proposed robust fault diagnosis scheme is applied to a satellite dynamic system and simulation results illustrate its satisfactory performance. I. INTRODUCTION Due to the importance of safety and reliability of the control systems in many complex system applications, fault detection, isolation, identification and accommodation have received considerable attention over the past two decades. Prompt fault detection indicates the occurrence of faults. Correct fault isolation determines the locations of the faults. Precise fault identification specifies the characteristics of the faults. All of this work helps to develop fault accommodation strategies to guarantee failsafe operations of the control systems. In the categories of fault diagnosis (FD) techniques, ana- lytical redundancy approaches based on linear or nonlinear models have been widely considered. Fruitful contributions are summarized in the books [1], [2], [3]. In general, model-based fault diagnosis methods generate a residual via comparing the measurable output of a system with that of its mathematical model. Then, fault diagnostic decisions are made based on the residual. Efficient fault diagnosis depends on the robustness of the residual with respect to system uncertainties. For linear systems, robust fault diagnosis can be obtained via unknown input observers and eigenstructure assignment methods, both of which decouple the effect of the uncertainties from the residual. For nonlinear systems, learning approaches based FD schemes, which use neural networks [4], [5] or adap- tive observers [6], [7], [8] to estimate faults have been investigated in many literatures. Dead-zone operators are always adopted in the learning algorithms to achieve a robust estimation of the faults [9], [10]. Owing to the inherent robustness to system uncertainties, sliding mode observers have been applied to the fault detec- tion and diagnosis [11], [12], [13]. In order to guarantee the stability of the fault diagnosis scheme, the bound of The authors are with the School of Engineering Science, Simon Fraser University, Vancouver, B.C., V5A 1S6, Canada. saif@cs.sfu.ca system uncertainties is usually estimated and involved in the design of the switching gain. However, a large amount of chattering occurs when this method is implemented by digital computers at a given sampling frequency. Thus, a variety of approaches have been proposed to reduce the unnecessary chattering. One method is to use a continuous saturation function rather than the discontinuous sign function. Other methods adaptively estimate the bound of the system uncer- tainties [14] or construct an adaptive switching gain [15]. This work establishes a nonlinear observer and applies it to the fault diagnosis of a class of nonlinear systems. The observer consists of an adaptive sliding mode term and a neural state space (NSS) model. The sliding mode term is used to eliminate the effect of the system uncertainties, and the NSS model is adopted to identify various faults. In this fault diagnosis scheme, the adaptive switching gain avoids unnecessary chattering, and the iterative learning algorithm can be easily implemented. Additionally, This fault diagnosis scheme is not only robust to the system uncertainties, but also able to identify various faults with satisfactory performance. Finally, the application of the proposed FD scheme to a satellite control system demonstrates its effectiveness. II. PROBLEM FORMULATION The class of nonlinear dynamic systems under this study is described by ˙ x i (t)= ξ i (x 1 ,x 2 , ··· ,x n )+ B i (y,u)+ η i (x, u, t) +f i (y, u, t) ˙ xi+1(t)= xi (t), (i =1, 3, ··· ,n − 1) y(t)=[x 2 ,x 4 , ··· ,x n ]  , (1) where x =[x 1 , ··· ,x n ]  ∈ n with x(0) = x 0 is the state vector, u ∈ m is the control input vector, and y ∈ p is the measurable output vector of the system. The vector ξ (x)= [ξ 1 (x),x 1 , ··· ,ξ n−1 (x),x n−1 ]  is defined as the state func- tion, B(x, u)=[B 1 (y,u), 0, ··· ,B n−1 (y,u), 0]  denotes the input function, η =[η 1 (t), 0, ··· ,η n−1 (t), 0]  represents the uncertainty vector, and f =[f 1 (t), 0, ··· ,f n−1 (t), 0]  is the state fault vector. In a vector form, (1) can be rewritten as ˙ x(t)= ξ(x(t)) + B(y,u)+ η(x, u, t)+ f (y, u, t) y(t)= Cx(t), (2) where η :  n × m × + → n , f :  p × m × + → n are all smooth vector fields. Remark 1: The system (1) only contains modeling uncer- tainties and state faults, and our work focuses on the robust diagnosis of state faults in the presence of state uncertainties. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 Seville, Spain, December 12-15, 2005 ThIB20.4 0-7803-9568-9/05/$20.00 ©2005 IEEE 7668