Relative-velocity-free output-feedback consensus control for multiple Euler–Lagrange systems based on high-order extended state observer

In this paper, an output-feedback controller is devised with the assistance of two types of observers to deal with the leader-following consensus control problem of multiple Euler–Lagrange (EL) systems, which are subject to model uncertain parameters, external disturbances, and unmeasured velocity. First, a local high-order extended state observer is put forward to estimate both the compound disturbance and unmeasured velocity for each EL system, and the boundedness of the estimation errors can be guaranteed under standard assumptions. Then, a novel distributed finite/fixed-time observer is proposed to observe the leader’s position and velocity without using the relative velocity information. Based on these two kinds of observers, a distributed output-feedback control algorithm, which does not depend on any global information, is constructed using the back-stepping method, while some sufficient conditions are derived to guarantee that tracking errors are semi-globally uniformly ultimately bounded. Finally, the effectiveness of the presented control scheme is further verified by a numerical simulation.