Convergence of weighted minimum variance N-step ahead prediction/control schemes

Dual problems of N-step-ahead prediction and control of plants with a series N delay are studied for the case when there are parameter uncertainties in the signal generating system. In particular, novel variations of existing schemes are proposed with the variations introduced to guarantee global convergence. The convergence theory, which applies martingale convergence results to N decomposed terms consisting of the parameter and state estimation errors, guides the selection of weighting coefficients in a weighted least squares approach. There are thus attractions over competitive schemes involving a bank of N interleaved parameter udpate recursions with their additional memory requirements.