  The present paper proposes a novel broadcast control (BC) law for multi-agent
coordination. A BC framework has been developed to achieve global coordination
tasks with low communication volume. The BC law uses broadcast communication,
which transmits an identical signal to all agents indiscriminately without any
agent-to-agent communication. Unfortunately, all of the agents are required to
take numerous random actions because the BC law is based on stochastic
optimization. Such random actions degrade the control performance for
coordination tasks and may invoke dangerous situations. In order to overcome
these drawbacks, the present paper proposes the pseudo-perturbation-based
broadcast control (PBC) law, which introduces multiple virtual random actions
instead of the single physical action of the BC law. The following advantages
of the PBC law are theoretically proven. The PBC law achieves coordination
tasks asymptotically with probability 1. Compared with the BC law, unavailing
actions are reduced and agents' states converge at least twice as fast.
Increasing the number of multiple actions further improves the control
performance because averaging multiple actions reduces unavailing randomness.
Numerical simulations demonstrate that the PBC improves the control performance
as compared with the BC law.
