Prescribed-Performance Control Design for Pure-Feedback Nonlinear Systems with Most Severe Uncertainties

Abstract

This paper is devoted to the control design for uncertain pure-feedback nonlinear systems. Remarkably, the systems under investigation allow the completely nonaffine appearance of the virtual/actual controls and can be subjected to serious nonparametric uncertainties and unknown control directions, which are arguably the most severe uncertainties. Even so, a prescribed-performance control design scheme is proposed for the systems, where the system states are ensured to evolve within prescribed funnels. By suitably choosing the prescribed funnels, the controller designed can not only accomplish the basic steady performance on stabilization/tracking but also achieve other prescribed performance to guarantee the efficiency and reliability of the systems. Particularly, based on the scheme with suitably choosing the prescribed funnels, global stabilization with prescribed convergence rate and global/semiglobal practical tracking with prescribed transient performance (arrival time/maximum overshoot) are achieved for the uncertain pure-feedback systems.