Interval observer-based methodology for passive fault tolerant control of linear parameter-varying systems

Abstract

The paper deals with passive fault tolerant control for linear parameter varying systems subject to component faults. Under the assumption that the faults magnitudes are considered unknown but bounded, a novel methodology is proposed using interval observer with an [Formula: see text] formalism to attenuate the effects of the uncertainties and to improve the accuracy of the proposed observer. The necessary and sufficient conditions of the control system stability are developed in terms of matrix inequalities constraints using Lyapunov stability theory. Based on a linear state feedback, a fault tolerant control strategy is designed to handle component faults effect as well as external disturbances and preserve the system closed-loop stability for both fault-free and component faulty cases. Two simulation examples are presented to demonstrate the effectiveness of the proposed method.

Tight interval state estimate for discrete‐time descriptor linear systems

“…In this subsection, two comparison results on the DC motor system are presented to illustrate the performance of the proposed methods. First, we compare the simulation results of the symmetric‐box‐based set‐estimator (Algorithm 1) with those obtained by the interval observer approach introduced in Reference 17. Second, the zonotopic‐based set‐estimator (Algorithm 3) is compared with the zonotopic method presented in Reference 35.…”

“…Second, the zonotopic‐based set‐estimator (Algorithm 3) is compared with the zonotopic method presented in Reference 35. The simulation results are illustrated in Figures 8 and 9 where solid black lines correspond to the results of the application of methods in References 17 and 35, while the dashed lines represent those provided by our proposed methods.…”

“…Comparison state estimation results of symmetric‐box‐based set‐estimator (Algorithm 1) with method proposed in Reference 17. (A) $$$ {x}_1 $$$ first state variable, (B) $$$ {e}_1 $$$ element‐wise width, (C) $$$ {x}_2 $$$ second state variable, (D) $$$ {e}_2 $$$ element‐wise width, (E) $$$ {x}_3 $$$ third state variable, (F) $$$ {e}_3 $$$ element‐wise width.…”

“…Based on this assumption, numerous methods have been proposed to design such estimators. For example, polytopes, 12,13 ellipsoids, [14][15][16] intervals, [17][18][19] and zonotopes [20][21][22] are used to enclose, at each time instant, the actual state of the system. 23 On the other hand, descriptor systems have received much attention in the last decades as a general class of systems.…”

“…Based on this assumption, numerous methods have been proposed to design such estimators. For example, polytopes, 12,13 ellipsoids, 14–16 intervals, 17–19 and zonotopes 20–22 are used to enclose, at each time instant, the actual state of the system 23 …”