Hierarchical predefined‐time bipartite tracking of Euler–Lagrange systems over a signed graph

Abstract

AbstractThis paper addresses the hierarchical predefined‐time bipartite tracking problem in networked Euler–Lagrange systems (ELSs) over a signed graph, considering the presence of outer disturbances and dynamic uncertainties. An algorithm about the novel hierarchical predefined‐time control (HPTC) is presented here, which aims to guide the states of two opposing subgroups of the ELSs to achieve the leader's trajectory while the signs are opposite. The algorithm allows for flexibility in setting the desired settling time for the system, the upper bound of which is simple to be predetermined in advance and adjusted like other parameters.Through Lyapunov stability analysis, a sufficient criteria is established for achieving predefined‐time bipartite tracking problem. Finally, numerical simulations are conducted to illustrate the effectiveness and performance of the developed methods.