A Robust Direct Adaptive Controller

This paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics. The algorithm is designed based on the reduced-order plant, which is assumed to be minimum phase and of known order and relative degree, but is analyzed with respect to the overall plant which, due to the unmodeled dynamics, may be nonminimum phase and of unknown order and relative degree. It is shown that if the unmodeled dynamics are sufficiently small in the low-frequency range, then the algorithm guarantees boundedness of all signals in the adaptive loop and “small” residual tracking errors for any bounded initial conditions. In the absence of unmodeled dynamics, the residual tracking error is shown to be zero.