Bipartite tracking for Euler–Lagrange systems via prescribed-time hierarchical control based on the matrix-weighted signed digraphs

Abstract

The goal of this article is to investigate the bipartite tracking control problem using a prescribed-time convergence method for Euler–Lagrange systems (ELSs) with external disturbances. Agent interactions are represented by a matrix-weighted signed directed graph. There are not only cooperative but also adversarial interactions. An essential component of the system, the prescribed-time hierarchical control (PTHC) algorithm, including a more general time-varying function, is newly developed to guarantee that all agents converge to the same leader state but with opposite signs within a prescribed time. The salient feature of the introduced method lies in the fact that the convergence time of the control objective can be prespecified by the user. The state transformation, the property of the matrix-weighted Laplacian, and the generalized Lyapunov stability argument are employed to theoretically validate the proposed algorithms. Finally, the effectiveness of the algorithm is confirmed through the execution of numerical examples.