Robust <i>H</i>_∞ sliding mode observer‐based fault‐tolerant control for One‐sided Lipschitz nonlinear systems

摘要

Abstract This paper presents fault tolerant controllers for a class of one‐sided Lipschitz nonlinear systems with external disturbances. A sliding mode observer (SMO) is integrated with the H ∞ filtering approach as the fault detection and isolation module. The problem is investigated in the presence of faults and disturbances simultaneously. The H ∞ ‐SMO is capable of approximating faults accurately, while reducing the effect of disturbances in the estimation of the state vector and occurred faults. Accordingly, using only a single SMO, the estimation error of the state vector and faults can be made simultaneously arbitrarily small. In addition, to deal with the weighted bilinear form appearing in the one‐sided Lipschitz condition, the quadratically inner bounded condition presented in the literature is employed in this paper as a useful solution. The proposed method guarantees the stability of the overall closed‐loop system, and after a short transient time, the estimation errors for state vector and fault signal converge to a small neighborhood of the origin. The effectiveness of the presented algorithm is confirmed in two examples including a single arm robot with a flexible joint and a numerical simulation.