Identification and Predictive Control by p-norm Minimization

Real time system parameter estimation from the set of input-output data is usually solved by minimization of quadratic norm errors of system equations – known in the literature as least squares (LS) or its modification as total least squares (TLS) or mixed LS and TLS. It is known that the utilization of the p-norm (1?p<2) instead of the quadratic norm suppresses the wrong measurements (outliers) in the data. This property is shown for different norms, and it is shown that the influence of outliers is suppressed if p ›1. Also optimal predictive control utilizing p-norm minimization of the criterion is developed, and the simulation results show the properties of such control.