Online Adaptive Learning Solution of Multi-Agent Differential Graphical Games

Distributed networks have received much attention in the last year because of their flexibility and computational performance. The ability to coordinate agents is important in many real-world tasks where it is necessary for agents to exchange information with each other. Synchronization behavior among agents is found in flocking of birds, schooling of fish, and other natural systems. Work has been done to develop cooperative control methods for consensus and synchronization (Fax and Murray, 2004; Jadbabaie, Lin and Morse, 2003; Olfati-Saber, and Murray, 2004; Qu, 2009; Ren, Beard, and Atkins, 2005; Ren, and beard, 2005; Ren, and Beard, 2008; Tsitsiklis, 1984). See (Olfati-Saber, Fax, and Murray, 2007; Ren, Beard, and Atkins, 2005) for surveys. Leaderless consensus results in all nodes converging to common value that cannot generally be controlled. We call this the cooperative regulator problem. On the other hand the problem of cooperative tracking requires that all nodes synchronize to a leader or control node (Hong, Hu, and Gao, 2006; Li, Wang, and Chen, 2004; Ren, Moore, and Chen, 2007; Wang, and Chen, 2002). This has been called pinning control or control with a virtual leader. Consensus has been studied for systems on communication graphs with fixed or varying topologies and communication delays.