Design of an adaptive dynamic sliding mode control approach for robotic systems via uncertainty estimators with exponential convergence rate

Abstract

In this work, an adaptive dynamic sliding mode control approach is proposed for robotic systems via uncertainty estimators with exponential convergence rate. The uncertainties are estimated using various uncertainty estimators such as the Fourier series expansion, Legendre polynomials and adaptive fuzzy systems. Also, for each uncertainty estimator, the approximation error is compensated. The adaptation laws are derived using a stability analysis. Moreover, the asymptotic convergence of the tracking error and the boundedness of all closed-loop signals are guaranteed. The novelty of this paper is proposing a positive exponential function for the convergence rate of the adaptation rules to prevent from initial high voltages originated from large initial tracking errors. Another novelty of this paper is presenting a robust control term for the truncation error that improves the accuracy of the control system. Analysis of simulations reveals the effectiveness of the proposed method in terms of fast disturbance rejection and negligible tracking error.