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Global Practical Tracking for High-Order Uncertain Nonlinear Systems with Unknown Control Directions

This paper addresses the global practical tracking problem for a class of high-order uncertain nonlinear systems with unknown control directions under fairly weak conditions. Although the stabilization problem has been studied for the systems, the tracking problem remains unsolved up to now mainly because of the essential differences between stabilization and tracking problems when control directions are unknown. In this paper, by introducing a novel coordinate transformation and new updating laws, an approach is presented for the first time to design a continuous adaptive controller to make the tracking error prescribed arbitrarily small after a finite time and simultaneously to keep all the closed-loop states bounded. It is worth emphasizing that the proposed adaptive tracking control design scheme is motivated by the recent tracking works, inspired by the ideas of universal control and dead zone and obtained by the approaches of Nussbaum-gain and adding a power integrator. Most importantly, this paper removes the basic assumption that the control directions are precisely known in the related tracking works, without additional conditions imposed on the systems and the reference signal.