Global Asymptotic Tracking Controller With Prescribed Performance for Uncertain Nonlinear Systems With Unknown Control Directions

ABSTRACT In this paper, we revisit the tracking problem of a nonlinear system subject to unknown time‐varying parameters, external disturbances and unknown control directions, and propose a novel adaptive controller that guarantees boundedness of all closed‐loop signals and achieves asymptotic output tracking with prescribed performance. With the help of Nussbaum functions, the control does not require the knowledge of the control directions. The introduction of an error tuning function enables global asymptotic tracking, instead of semi‐global results seen in some existing literature, and satisfaction of the prescribed performance after any prescribed, arbitrarily short, time period. The use of an asymptotic step function helps the controller to achieve asymptotic tracking as the sign function does in inducing the reaching condition in the traditional sliding mode control, while many related works only ensure the tracking error to evolve into a small neighborhood of the origin. Furthermore, viewing the unknown parameters, derivatives of the virtual control laws and higher‐order derivatives of the reference output as disturbance‐like terms to be compensated adaptively along with the disturbances, the proposed design obliviates the utilization of approximation structures, the derivatives of the virtual control laws and the higher‐order derivatives of the reference output and, thus, simplifies the design and implementation of the controller. Finally, simulation results validate the theoretical conclusions summarized above.