ABSTRACT
Over the last two decades, the rejection problem of unknown neutral stable disturbances for nonlinear systems has attracted considerable attention. A prevalent control strategy is the well-known output regulation theory, where the unknown disturbances can be treated as an autonomous exosystem ([12, 106, 112]). The compensation of the disturbances can be realized in the feedback path with the celebrated internal model principle. If the parameter is unknown, the situation becomes complex. For linear systems, the adaptive regulator is designed in [145] which tunes the internal model of the unknown exosystem so that it will asymptotically reproduce the unknown exosystem and the corresponding open-loop control signal. In [16], periodic disturbances with uncertain frequency are cancelled using an adaptive internal model based on singular perturbation and averaging theories, and local exponential stability can be obtained. The more general case where there exists an uncertain dynamic in a system model has been studied in [210].
