Adaptive sliding mode fault tolerant control design for uncertain nonlinear systems with multiplicative faults: Takagi–Sugeno fuzzy approach

Abstract

The present article deals with adaptive sliding mode fault tolerant control design for uncertain nonlinear systems, affected by multiplicative faults, that is described under Takagi–Sugeno fuzzy representation. First, we propose to conceive robust adaptive observer in order to achieve states and multiplicative faults estimation in the presence of nonlinear system uncertainties. Under the nonlinear Lipschitz condition, the observer gains are attained by solving the multi-objective optimization problem. Second, sliding mode controller is suggested to offer a solution of the closed-loop system stability even the occurrence of real fault effects. The main objective is to compensate multiplicative fault effects based on output feedback information. Sufficient conditions are developed with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> performances and expressed as a set of linear matrix inequalities subject to compute controller gains. Finally, simulation results, using the nonlinear model of a single-link flexible joint robot system, are given to illustrate the capability of the suggested fault tolerant control strategy to treat multiplicative faults.