An adaptive controller of discrete-time systems with unknown control direction

In this paper, a novel adaptive control scheme is proposed for a class of discrete-time nonlinear systems with unknown control direction. Without using the discrete Nussbaum gain, the proposed scheme directly estimates the unknown control gain instead of its inverse. The singularity of the control law is overcome by using the previous estimated control gain when the current one falls into a small neighborhood of zero. The proposed adaptive control, with using a modified projection algorithm, can guarantee boundedness of all the closed-loop signals and convergence of the tracking error. An illustrative example is presented to verify effectiveness of the proposed scheme.