Global Feedback Regulation for a Class of Uncertain Nonlinear Systems via Integral Control: A Gain Control Technique

This article studies the global feedback regulation problems for triangular nonlinear systems perturbed by matched disturbances and modeling uncertainties with unknown system parameters. Instead of constructing extended state observers, new integral controllers composed of an integral dynamic are constructed to make all states of the uncertain systems bounded and asymptotically converge to zero. First, an integral dynamic is constructed and a new state transformation is introduced, which transforms the triangular nonlinear systems into a class of auxiliary intermediate systems. Second, by using the time-varying gain technique, designing regulating controllers for the auxiliary intermediate systems is converted into designing a dynamic parameter for a class of new systems. Third, with the help of the Lyapunov stability theorem and the characteristics of designed dynamic parameter, it is provided that the boundness of the new systems yields the regulation of the auxiliary intermediate systems, which further indicates the global feedback regulation of the considered systems. Two physical system examples are given to demonstrate the effectiveness of the proposed controllers.