Barrier Lyapunov function-based adaptive asymptotic tracking of nonlinear systems with unknown virtual control coefficients

Abstract

This paper is devoted to the adaptive asymptotic tracking control for a class of uncertain nonlinear systems with parametric uncertainties. The presence of unknown virtual control coefficients and full-state constraints makes the systems in question essentially different from those in the related works. By incorporating the lower bounds of virtual control coefficients into the barrier Lyapunov functions (BLFs), two adaptive backstepping control design schemes are proposed based on tuning function method, bound estimation approach and some smooth functions, which makes the controller powerful enough to compensate the unknown virtual control coefficients and parametric uncertainties. We also show that the overall control strategy achieves three objectives on system performance: (a) the asymptotic convergence with zero tracking error is ensured; (b) all signals in the closed-loop systems are bounded; and (c) the full-state constraints are not violated for all the time. Finally, the effectiveness of the proposed method is shown by simulation examples.