Robust Identification of Bilinear Systems

Abstract

<p>This thesis has been directed towards the problem of robust identification of bilinear systems. Special attention has been given to the robust estimation problem of expansion coefficients of orthogonal function series.</p> <p>A thorough survey of the robust identification of linear systems has been made. The existing robust identification methods have been critically evaluated. Six robust on-line identification algorithms have been proposed for not only parameter identification but also state estimation of bilinear systems. The convergence of these algorithms is theoretically established by using two different techniques. The simulation examples included in this thesis demonstrate the robustness of these methods.</p> <p>An off-line method, the robust iterative least squares method with modified results (RILSMMR), has been developed for identification of both linear and bilinear systems. A convergence proof for this method has also been provided. The advantage of this method over the currently used robust methods has clearly been confirmed by simulation.</p> <p>The RILSMMR has successfully been used for the first time to estimate the expansion coefficients of orthogonal function series when the time series are contaminated by not only noise but also outliers. This makes it possible to use orthogonal functions to solve various application problems in different areas. Hitherto, these problems have been unaddressed due to the presence of noise and outliers. Two examples using orthogonal functions, namely, Walsh and block-pulse functions have been utilized for the first time for the robust identification of both linear and bilinear systems. The convergence analysis of these approaches have been given on the basis of the convergence proof of the RILSMMR. The simulation examples demonstrate the advantage of these approaches over their non-robust counterparts.</p> <p>Finally, comments and recommendations for further research have been included.</p>