Adaptive robust control of a class of nonlinear strict-feedback discrete-time systems with unknown control directions

In this paper, adaptive control is studied for a class of nonlinear discrete-time systems in strict-feedback form with unknown control directions. The system is transformed to an nn-step ahead predictor, based on which an adaptive control employing the predicted future states has been proposed. The discrete Nussbaum gain is exploited to overcome the difficulty caused by unknown control directions. The proposed control guarantees the boundedness of all the closed-loop signals and the output tracking error can be made to converge to zero if the system is free of external disturbance. The effectiveness of the proposed control is demonstrated in the simulation.