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In the literature, most of the consensus methods require the control directions of all agents to be known. This paper deals with the distributed consensus problem without such requirements for networked Lagrangian systems subjected to uncertain dynamics. Unknown control directions are nonidentical in the sense that the control direction related to each control input in an individual Lagrangian system can be different and unknown as well as that the control directions for different Lagrangian systems are allowed to be distinct. Regarding the communication topology, the only requirement is to contain a fixed directed spanning tree. Based on the estimated consensus value, novel auxiliary sliding mode variables are constructed and applied to develop the distributed adaptive consensus control scheme. It is proved by adopting the special properties of the Laplacian matrix on directed graphs and matrix theory that global uniform boundedness of all closed-loop signals and the asymptotic consensus can be achieved. Simulations on networked two-link revolute joint arms are provided to verify the validity of the proposed scheme.

Distributed Consensus of Networked Lagrangian Systems With Unknown Nonidentical Control Directions