Multimodel Approach to Robust Identification of Multiple-Input Single-Output Nonlinear Time-Delay Systems

The robust multimodel solution for multiple-input single-output nonlinear time-delay systems identification with polluted outputs is derived in this article. First, all the local autoregressive exogenous models are preidentified at the working points; then, the global system model is built by interpolating the local models with a smoothing strategy. The outliers and input time-delays which often increase the nonideality of process data are both considered. To cope with the outliers, the Laplace distribution is reutilized to describe the output measurement process and the negative impact resulted from each outlier imposed on parameter estimation can be suppressed through automatically assigned small weight. The parameter estimation procedure is realized with the expectation-maximization algorithm and the joint posterior probability of all input delays is also maximized to calculate the unknown input time-delays. With the verifications on a numerical example and the continuous fermentation process, the validity of the proposed approach is proved.