Two-Layer Distributed Formation-Containment Control of Multiple Euler–Lagrange Systems by Output Feedback

This paper addresses the distributed formation-containment (DFC) problem for multiple Euler-Lagrange systems with model uncertainties via output feedback in both constant and time-varying formation cases. First, a novel definition of the DFC problem is proposed using a two-layer framework. Since only parts of the followers can acquire the states of the dynamic leader, we design a distributed finite-time sliding-mode estimator to obtain accurate estimations of the desired position and velocity for each agent. Next, to deal with the absence of velocity sensors, we propose two DFC control laws combined with the high-gain observer for the leaders and the followers, respectively, while the time-varying formation in the first layer and the leader-based containment in the second layer can be achieved. Further, the adaptive neural networks are applied to deal with the model uncertainties due to their superior approximation capability. The uniform ultimate boundedness of all the state errors can be guaranteed by Lyapunov stability theory. In addition, a unified framework is given which can be transformed to four other basic distributed problems. Finally, simulation examples are presented to illustrate the feasibility of the theoretical results.