Abstract: A discrete-time adaptive control law for stabilization, command following, and disturbance rejection that is effective for systems that are unstable, MIMO, and/or nonminimum phase. The adaptive control algorithm includes guidelines concerning the modeling information needed for implementation. This information includes the relative degree, the first nonzero Markov parameter, and the nonminimum-phase zeros. Except when the plant has nonminimum-phase zeros whose absolute value is less than the plant's spectral radius, the required zero information can be approximated by a sufficient number of Markov parameters. No additional information about the poles or zeros need be known. Numerical examples are presented to illustrate the algorithm's effectiveness in handling systems with errors in the required modeling data, unknown latency, sensor noise, and saturation.

Abstract: A method and system for attenuating the effects of unknown, unmeasurable and time-varying exogenous disturbances on multiple-input multiple-output dynamical systems are described. The disturbance rejection system is characterized in terms of an ARMARKOV or predictive model controller. The parameters of this controller are revised in real time at discrete time steps so as to generate an input to the dynamical system that attenuates the effect of the exogenous disturbance on any chosen set of measured outputs of the dynamical system. The method for revising the controller parameters involves the steps of defining a novel retrospective cost function based on windows of past data, calculating a gradient that is based on this cost function, and using an implementable adaptive step size that brings the controller parameters closer to optimal controller parameters after each revision.