Improvement of transient performance in MRAC by memory regressor extension

Abstract

The paper addresses the problem of transient performance improvement of direct model reference adaptive control (MRAC) of discrete linear time-invariant (LTI) plants. Two solutions to the problem are proposed and use the certainty equivalence principle and the idea of regressor recording over a past period of time. The first solution is based on the principle of augmented error, while the second one uses new scheme of high order tuner generating predicted values of adjustable parameters. The recording of the past regressor is provided by application of a special SISO filter (linear operators with “memory”) to the closed-loop error model. It is proven and demonstrated by numerical examples that the proposed solutions can provide asymptotic (not exponential) convergence of the adjustable parameters under some simple condition which is weaker than the persistent excitation one. The proposed solution can be considered as a generalization of the identification/adaptation algorithm proposed by Kreisselmeier for continuous systems [21, 22].