Distributed Coordination Control of Position-constrained Euler-Lagrangian Systems with Unknown Control Directions Under a Directed Graph

For an actual control system, the position information is usually an indispensable physical quantity for feedback control, while in an actual project, the position quantity is generally constrained. This paper discusses the distributed leader-following consensus control problem of networked Euler-Lagrangian systems (ELSs) both with unknown control directions and position constrains under a directed topology. Two novel types of barrier Lyapunov functions together with a Nussbaum-type gain function are employed to design distributed leader-following consensus protocol under a directed graph in this paper. One Lyapunov function is used to ensure that all the signals in the closed-loop system are bounded and the other is designed to prove that the consensus tracking errors of all the followers are uniformly ultimately bounded (UUB) and can be adjusted arbitrarily small. Meanwhile, according to the analysis of the tracking procedure, the security problem of position constraints are always satisfied. Finally, simulation examples are given to verify the effectiveness of the proposed algorithms in this paper.