Almost fast finite‐time adaptive tracking control for a class of full‐state constrained pure‐feedback nonlinear systems

Abstract

In this article, a novel almost fast finite-time adaptive tracking control scheme is proposed for a class of full-state constrained pure-feedback nonlinear systems based on barrier Lyapunov functions (BLFs). First, by employing the mean value theorem, the pure-feedback systems are converted to the strict-feedback structure with nonaffine terms. Then, by fusing adaptive backstepping technique and BLFs, the design difficulties caused by the nonaffine terms and full-state constraints are overcome. Furthermore, according to the predeveloped almost fast finite-time stability criterion, it is proved that the tracking error can converge to a small compact set and all signals of the closed-loop system can be bounded in an almost fast finite time. Finally, a simulation example of a single-link robot is presented to verify the effectiveness of the proposed control scheme. K E Y W O R D S almost fast finite time control, barrier Lyapunov functions, full-state constraints, pure-feedback nonlinear systems 1 INTRODUCTION In recent decades, due to the wide existence of nonlinear systems in practical engineering applications, nonlinear systems has been widely concerned by researchers in the field of control. However, compared with linear systems, the stability analysis and controller design of nonlinear systems are more difficult and complex. Fortunately, an effective analysis and design tool for nonlinear systems, the backstepping technique, was proposed in Reference 1 first. After this pioneering work, many excellent works have been achieved through the utilization of backstepping technology, such as References 2-7. As we all know, it is inevitable that uncertainties are contained in the practical plants. Nevertheless, the uncertainties in nonlinear systems were not considered in the above works. In order to deal with the uncertain parameters in the nonlinear system, the adaptive backstepping control algorithm was developed by properly designing the adaptive laws. Subsequently, the classical adaptive backstepping control algorithm has been employed to get many important results, for instance, References 8-23. Although these above works have made great contributions to the stability analysis and design of nonlinear systems, they have hardly utilized to the nonlinear pure-feedback systems. The material in this article was not presented at any IFAC meeting.

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