Simultaneous actuator and sensor fault estimation for discrete‐time Lipschitz nonlinear systems in finite‐frequency domain

Abstract

SummaryThis paper addresses the problem of actuator and sensor fault reconstruction simultaneously with finite-frequency specifications for discrete-time Lipschitz nonlinear systems. First, an augmented system description is given by extending the sensor fault as an auxiliary state vector. Then, a multiobjective unknown input proportional-integral observer is designed, and the nonlinear error dynamics are transformed into a linear parameter-varying system based on the use of a reformulated Lipschitz property. Sufficient conditions for the design of a fault estimator with 2 finite-frequency H ∞ performances are derived in terms of linear matrix inequalities where a slack variable is introduced to reduce the conservativeness of the design. The proposed method can provide less restrictive linear matrix inequality conditions and get a better fault estimation performance than the existing one in the full frequency domain. Simulation results are given to show the effectiveness of the proposed techniques.

Reduced‐order simultaneous state and fault estimator based fault tolerant preview control for discrete‐time linear time‐invariant systems

“…On the one hand, as mentioned before, there are three main kinds of SSFE structures in the literature, i.e. IDO-SSFE [19][20][21][22][23][24], UIDO-SSFE [25][26][27], and RF-SSFE [28][29][30][31]. These SSFEs have their individual characteristics.…”

“…In the literature, many representative results on simultaneous state and fault estimation have been reported [16][17][18]. From the view of estimator structures and design steps, three main kinds of simultaneous state and fault estimator (SSFE) can be concluded: innovation-driven observer-based SSFE (IDO-SSFE) [19][20][21][22][23][24], unknown input decoupling observer-based SSFE (UIDO-SSFE) [25][26][27], and robust filter-based SSFE (RF-SSFE) [28][29][30][31]. Depending on the design requirements, these SSFEs can be further synthesised as full-order form and reduced-order form.…”

“…In the literature, two kinds of methods to design reduced-order SSFEs can be found. One is to perform system model reduction followed by deigning corresponding-order IDO-SSFE [20,21,32], and the other is to directly design reduced-order RF-SSFE [28,30,33]. Unfortunately, the model-reduction manipulation in designing reduced-order IDO-SSFE requires that the output equation of system is free of noise or disturbance, which largely limits its application scope.…”

Towards Simultaneous Actuator and Sensor Faults Estimation for a Class of Takagi-Sugeno Fuzzy Systems: A Twin-Rotor System Application

“…Indeed, a recent state-of-the-art overview clearly indicates the trends for handling multiple simultaneous actuator and sensor fault estimation for nonlinear systems. Indeed, Gu et al [ 19 ] converted an original Lipschitz system into a Linear Parameter Varying (LPV) one by a suitable reformulation of the Lipschitz property. The resulting design approach provides optimal fault estimates according to criterion within the frequency domain.…”

Towards Robust Simultaneous Actuator and Sensor Fault Estimation for a Class of Nonlinear Systems: Design and Comparison

“…Indeed, a recent literature review clearly indicates the trends for settling simultaneous actuator and sensor fault estimation for nonlinear systems. In particular, [19] transformed a nonlinear Lipschitz system into a Linear Parameter Varying (LPV) one using the so-called reformulated Lipschitz property. The proposed design strategy provides optimal H ∞ fault estimates in the finite-frequency domain.…”