Nonlinear Parity Approach to Fault Detection in Nonlinear Systems Using Unknown Input Observer

The following study presents a novel fault detection approach, based on nonlinear parity design using nonlinear unknown input observers, for a class of nonlinear systems in the presence of sensor noise. Initially, fault and noise are decoupled via splitting the system into two subsystems by a series of transformations on the states and output equations. The nonlinear unknown input observer estimates the states in the subsystem subject to sensor noise, while the states in the other subsystem are estimated with the proposed equation. The objective in this study is to ensure the asymptotic stability of the error dynamics using the Lyapunov method. Hence, the results are formulated in the form of bilinear matrix inequalities. At the same time, the nonlinear parity approach is employed to design residue signals in the subsystem subject to actuator/component faults. Sufficient conditions are established to guarantee the convergence of the state estimation error. The goal in the parity approach is to generate a specific residue indicating the difference between nominal and faulty states. Finally, three simulations are provided to illustrate the efficiency of the proposed algorithm.