Hierarchical estimator-based fixed-time and prescribed-time bipartite consensus of multiple Euler-Lagrange systems with a directed signed graph

This article addresses the fixed-time and prescribed-time bipartite consensus problem of Euler-Lagrange systems (ELSs) under a directed sign graph, taking into consideration both the parametric uncertainties and external disturbances. Novel hierarchical control algorithms employing estimator approaches are proposed to tackle the aforementioned challenges. More specifically, the control protocol is first designed to accomplish fixed-time bipartite consensus (Fix-TBC). The settling time obtained by using fixed-time control algorithm is restricted to its upper bound, but it may result in a conservative estimation of the bound. Consequently, it indicates the need for designing another control protocol to address the prescribed-time bipartite consensus (Pre-TBC) problem. By invoking Lyapunov stability theory, some sufficient conditions for achieving fixed-time and prescribed-time bipartite consensus of the ELSs are derived. Numerical examples are ultimately provided to demonstrate results.