Modified model reference adaptive control: Design, analysis and performance bounds

Abstract

Boundedness of all closed loop signals and asymptotic convergence of the tracking error to zero or to a residual set are the criteria that have been most commonly used to characterize the performance of model reference adaptive control schemes in the absence of persistently exciting signals. These criteria do not reveal the large transient oscillations often observed in simulations and do not exclude the possibility of bursting at steady state in the presence of small modelling errors. The purpose of this paper is to address the issue of performance by using two additional criteria to assess performance in the ideal and non-ideal situations. They are the mean square tracking error criterion and the L∞ tracking error bound criterion. We use these criteria to examine the performance of a standard model reference adaptive controller and motivate the design of a modified scheme that can have an arbitrarily improved nominal performance in the ideal case and in the presence of bounded input disturbances. It is shown that for these cases the modified scheme can provide an arbitrarily improved zero-state transient performance and an arbitrary reduction in the size of possible bursts that may occur at steady state. As in every robust control design the nominal performance has to be traded off with robust stability and therefore the improvement in performance achieved by the proposed scheme is limited by the size of the unmodelled dynamics, as established in the paper. Another expected limitation to nominal performance is sensor noise which due to space limitation is not examined here.