Convergence of multipredictor self-tuning regulators under mismatching conditions

Effects of multipredictor information in adaptive control are studied, particularly from the standpoint of plant structural uncertainties and unmodelled dynamics. It is shown, through a convergence analysis based on the O.D.E. method, that, for an ARMAX plant, a multipredictor based LQ self-tuning regulator, viz. the MUSMAR algorithm, if it converges, always converge to the local minima of the uncodintional quadratic cost constrained to the chosen regulator regressor. This result holds true, for a large enough regulation horizon, despite that standard recursive least-squares (R.L.S.) identifiers are used. When the plant order is correctly guessed or overestimated, MUSMAR only possible converging point coincides with the LQ optimal one, irrespectively of the true plant i/o transport delay.