Reliable $H_{\infty}$ Control of Linear Systems With Adaptive Mechanism

Abstract

This technical note studies the problem of designing reliable <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controllers with adaptive mechanism for linear systems. A new method for designing indirect adaptive reliable controller via state feedback is presented for actuator fault compensations. Based on the on-line estimation of eventual faults, the proposed reliable controller parameters are updated automatically to compensate the fault effects on systems. A notion of adaptive <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance index is proposed to describe the disturbance attenuation performances of closed-loop systems. The design conditions are given in terms of solutions to a set of linear matrix inequalities (LMIs). The resultant designs can guarantee the asymptotic stability and adaptive <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performances of closed-loop systems even in the cases of actuator failures. The effectiveness of the proposed design method is illustrated via a numerical example.