Hierarchical prescribed-time bipartite consensus for multiple Euler–Lagrange systems with input-to-output redundancy and directed matrix-weighted signed graph

Abstract

This paper studies the prescribed-time bipartite consensus problem for multiple Euler–Lagrange systems (MELSs) under directed matrix-weighted signed graph, in which input-to-output redundancy, external disturbances and uncertain dynamic terms have been taken into consideration. Firstly, this paper proposes the prescribed-time hierarchical control (PTHC) algorithm to tackle the aforesaid issue. It is worth pointing out that the convergence time can be arbitrarily prescribed based on actual engineering needs. Then, the corresponding sufficient conditions for achieving the prescribed-time bipartite consensus are obtained by invoking Lyapunov stability analysis. Eventually, the numerical simulation results are performed, which vividly reflect the effectiveness and feasibility of the developed control algorithm.