Fully Distributed Consensus of Multiple Euler–Lagrange Systems With Time-Varying Asymmetric Full-State Constraints

In this article, the consensus problem of multiple Euler–Lagrange (EL) systems with time-varying asymmetric full-state constraints under a directed graph is investigated in a fully distributed way, where the global information dependence is removed. First, to prevent the violation of the full-state constraints of each EL system, a nonlinear state-dependent transformation is adopted for both the leader and followers, where the constraints will not be violated as long as the transformed states remain finite. Then, a constrained nonlinear fully distributed observer is constructed using only neighbors' states, and an adaptive gain is designed to eliminate the dependence of the global information. The theoretical analysis is completed via constructing a novel integration-based Lyapunov function using a graph-based diagonal matrix, ensuring the achievement of consensus. Using the observed state, an adaptive backstepping state tracking control protocol is developed such that the position of each EL system can track the leader within a tolerable bounded region. Thus, the leader-following consensus of multiple EL systems with time-varying asymmetric full-state constraints is achieved. Simulation results are illustrated to show the feasibility and effectiveness of the proposed control scheme.