An adaptive fuzzy sliding‐mode control method for leader‐follower consensus of uncertain non‐square nonlinear systems

Abstract

Summary This study presents a new adaptive fuzzy sliding‐mode control method for the leader‐follower consensus problem of uncertain non‐square nonlinear systems in the presence of input saturation and dead‐zone. In the proposed approach, to transform the dynamic equations of every agent into fully‐actuated multi‐input/multi‐output nonlinear systems, some auxiliary inputs are defined based on the weighted pseudo‐inverse theory. Furthermore, the effects of input nonlinearities and the introduced terms due to the system transformation are considered as part of the unknown nonlinear dynamic model. The auxiliary input vector of each agent consists of a fuzzy term employed to approximate the unknown nonlinear model and a robust term to compensate for any possible mismatches. Therefore, by employing the adaptation laws proposed based on a Lyapunov function, the output vectors of the fuzzy systems and the upper bounds of the approximation errors are computed. The closed‐loop asymptotic stability is proved using the second Lyapunov theorem and Barbalat's lemma. Furthermore, the effectiveness of the proposed method is verified by the leader‐follower consensus control of a group of REMUS autonomous underwater vehicles.