Abstract
In this article, the distributed synchronization control problem is investigated for a class of uncertain nonlinear leader-following systems on directed graph, where unknown backlash-like hysteresis exists in the actuator of each follower and the topology of the graph is fixed. Based on basic graph theory, the principle of variable structure control and Lyapunov theory, by using the unknown smooth function approximation capability of type-2 fuzzy logic systems, a new distributed adaptive supervisory control design method is proposed such that all followers asymptotically synchronize to the leader and each synchronizing error is bounded. In the control method, with the help of supervisor control strategy, it is guaranteed that the resulting closed-loop signals including system states, respectively, belong to the corresponding compact sets, which is necessary for fuzzy approximation theory because it is on a compact set that an unknown smooth function can be approximated by fuzzy logic system. Furthermore, the adaptive compensation terms of the optimal approximation errors are adopted to reduce the effects of modeling errors. Finally, simulation results demonstrate the effectiveness of the proposed new design method.
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