Global stabilization of a chain of integrators with input saturation and disturbances: A new approach

In this article, we solve the problem of global stabilization for a chain of integrators in the presence of input saturation and disturbances. A novel and elegant approach to solve this problem, in the absence of disturbances, was proposed by Teel (1992) using saturation functions and coordinate transformation. With Teel's work as a foundation, many results have been proposed to improve the performance of controllers for a chain of integrators. Naturally, all such approaches also inherited the limitations of Teel's approach. Most importantly, in the presence of uncertainties and disturbances, the transformation introduced in Teel (1992) would considerably shrink the region where the controller is unsaturated and, severely limit the level of uncertainties and disturbances which can be tolerated. In order to overcome these difficulties, a conceptually different approach which does not rely on the coordinate transformation is presented in this work. Specifically, modified saturation functions are directly applied to the tracking error of actual states as opposed to transformed fictitious states to develop a globally stable controller. The proposed controller is less conservative in terms of the level of uncertainties and disturbances which can be handled. In addition, arbitrarily good disturbance rejection in the unsaturated region can be achieved theoretically. Comparative simulation studies performed on a third order integrator chain verified the effectiveness of the proposed scheme.