Adaptive control for full-states constrained nonlinear systems with unknown control direction using Barrier Lyapunov Functionals

Abstract

In this paper, a new adaptive back-stepping (BS) control technique based on barrier Lyapunov functions (BLFs) is proposed to manage a class of full-state constrained nonlinear systems subject to totally unknown directions and uncertain time-varying parameters. BLFs guarantee that all the system states are constrained in a predefined compact set and the tracking error can converge to a small zero neighborhood. Nussbaum’s gain technique is utilized to tackle the unknown control direction issue. Besides, a sufficiently smooth projection algorithm is adopted to estimate the unknown time-varying parameters, so as to ensure that the adaption laws are differentiable and bounded. The developed controller not only makes all the system states restrained in the compact set but also assures the smoothness and boundedness of all the signals of the closed-loop system. In addition, the sufficiently smooth projection algorithm and Nussbaum gain technique are combined with the BLF-BS control method for the nonlinear systems. Finally, the simulation example results verify the effectiveness and feasibility of the proposed control scheme.