Funnel Control of Uncertain High-Order Nonlinear Systems With Unknown Rational Powers

This article considers the funnel output tracking control for a class of high-order uncertain nonlinear systems with the powers of positive odd rational numbers, aiming to accomplish output tracking with prescribed accuracy when both the system nonlinearities and the powers of the system are unknown. For such a purpose, a robust funnel control algorithm, i.e., a continuous, static, and universal, state-feedback controller is explicitly constructed, which achieves the state errors evolving within the predesigned performance space. Benefits of the proposed funnel output tracking controller comparing with the current approaches lie in the fact that the exact knowledge of system nonlinearities, including generally required bounding functions, is not needed to be a priori. Moreover, all the powers in each high-order subsystem are permitted to be any unknown positive odd rational numbers as well. The efficacy of the developed algorithm is confirmed through two illustrative examples.