New Higher-Order Convergence Properties for Multivariable Model Reference Adaptive Control Systems

Abstract

For a general multi-input multi-output linear time-invariant system with unknown parameters, a multivariable model reference adaptive control (MRAC) scheme guarantees asymptotic output tracking, under some design conditions. This paper further shows a stronger higher-order convergence property for the signal components of the tracking error e (t) = [e 1 (t), e 2 (t), …, em (t)] T. It is proved that under the same MRAC design conditions, not only a tracking error component e i (t) but its up to q i th-order time-derivatives converge to zero, where q i is related to system's infinite zero structure characterized by the system interactor matrix ξ m (s). Both cases of a diagonal ξm (s) and a non-diagonal ξm (s) are studied in the paper, and the new MRAC tracking property is proved for different forms of the modified left interactor matrix.