Distributed cooperative control of position-constrained nonlinear systems under a directed graph

At present, the problem of leader-following consensus control under algebraic constraints is only studied in undirected graph, but not in a directed graph. This paper discusses the distributed leader-following consensus control problem of position-constrained networked Euler-Lagrangian systems (ELSs) under a directed graph. Based on adaptive control architectures, a distributed leader-following consensus algorithm is designed under a directed communication topology. Using a novel barrier Lyapunov function, the proposed control protocols can ensure that all the signals in the closed-loop system are bounded, as well as the consensus position tracking errors are uniformly ultimately bounded (UUB), and can be arbitrarily reduced by adjusting the control parameters. Moreover, during the process of consensus, the position constraints for each agent are never violated. Finally, the simulation results are discussed to illustrate the effectiveness of the theoretical analysis.