Adaptive guaranteed cost tracking control for high-order nonlinear systems based on fully actuated system approaches

Abstract

This paper considers the adaptive guaranteed cost tracking (AGCT) control problems for two classes of high-order nonlinear systems with unknown parameters. A new local smooth nonlinear function (LSNF) is introduced first, which provides an important mathematical tool for our controller design. Then, based on the LSNF and the high-order fully actuated (HOFA) system approaches, the AGCT controller is designed for HOFA system with unknown parameter, which guarantees that all of the states of the closed-loop HOFA system are globally bounded, and the tracking error is asymptotically convergent. Moreover, the upper bound of cost function (UBCF) characterizing the tracking performance can be arbitrarily preseted, and is completely independent of the system initial value and the unknown parameter, which significantly improves the tracking performance, and is difficult to achieve by using existing guaranteed cost control (GCC). Furthermore, an extra result, the AGCT controller for a class of strict-feedback systems with high-order form and unknown parameters, is obtained in this paper, which also guarantees that the system tracking error is globally asymptotically convergent with the arbitrarily preseted UBCF characterizing the tracking performance. Three simulation examples, including an inverted pendulum, are presented to show the effect and the superiority of the proposed method.