A Variable Gain Model-Independent Algorithm for Rendezvous of Euler-Lagrange Agents on Directed Networks

A variable-gain model-independent control law is proposed to solve the problem of rendezvous to a leader for a directed network of Euler-Lagrange agents. A sufficiency condition for stability is developed, requiring centralised design of the two control gains. Compared to existing results which use constant-gain model-independent controllers for directed networks, our work has two key differences. Firstly, the damping term may begin at zero, and increases only if rendezvous has not been achieved. Constant-gain controllers use conservative gain values which negatively impact convergence speed. Secondly, we introduce a novel method of analysing the Lyapunov derivative, which provides useful and unique insight into analysis of variable-gain controllers for multi-agent systems. Simulations are provided to show the effectiveness of the controller.