Distributed optimisation based on multi‐agent system for resource allocation with communication time‐delay

In this study, the distributed optimisation for solving resource allocation problem with both local bound and equality constraints is studied. A continuous‐time multi‐agent system with communication time‐delay is proposed for the resource allocation. First, to reduce communication cost, a new modified multi‐agent system is proposed inspired by previous work. Next, based on the system, the communication time‐delay is considered to reduce the communication cost and match real situation. Then, by choosing proper parameters, sufficient conditions are derived for convergence to the optimal solution of the distributed optimisation. Moreover, delay‐free case is also considered, which proves that the system is convergent based on directed communication graph by choosing proper parameters. Finally, simulation results demonstrate the characteristics of the system.