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This paper is mainly concerned with the leaderless consensus problem for nonlinear multi-agent systems (MAS) with unknown mismatched nonlinear dynamics and external disturbances. First, a novel adaptive controller is designed to achieve bounded consensus with a linear feedback term, the RBF neural network (RBFNN) adaptive approximation term, a discontinuous feedback term, and a state constraint term. Furthermore, on this basis, an observer-based robust uniform control scheme against disturbance is proposed to achieve the leaderless consensus of MAS with unmeasurable states under the directed graph. Compared with the previous works, the proposed controller is less conservative. Finally, two simulation-based examples are provided to verify the effectiveness of the proposed control scheme.