The Multilevel Hypernetwork Dynamics of Complex Systems of Robot Soccer Agents

A mathematical formalism is sketched for representing relational structure between agents. n-ary relations, n > 2, require hyper-networks, which generalise binary relation networks. n-ary relations on sets create structure at higher levels of representation to the elements, in multilevel systems. The state of a system is represented by its multilevel relational structure. The dynamics of a system are represented by state changes through time. These can be continuous with no change in the hyper-network topology, but often they are not. Controlling such systems involves taking actions intended to result in desirable state changes. The concept of multilevel hypernetwork can be applied to multi-agent systems in general.