Distributed coordination on state-dependent fuzzy graphs

Multiagent systems are increasingly becoming popular among researchers spanning multiple fields of study. However, existing studies only models communication interaction between agents as either fixed or switching topologies described by crisp graphs supported by algebraic graph theories. In this paper, we propose an alternative approach to describing agent interactions using fuzzy graphs. Our approach is aimed at opening up new research avenues and defining new problems in coordination control especially in terms of dynamics between agents’ states, graph topologies and coordination objectives. This paper studies distributed coordination on fuzzy graphs where the edge-weights modeling network topologies are dependent on the states of the agents in the network. In hindsight, the network weights are adjustable based on the situational state of the agents. First, we introduce the concept of fuzzy graphs and give some distinguishing features from the crisp or fixed graphs. Next, we provide some membership functions to define the state-dependent weights and finally we use some simulations to demonstrate the convergence of the proposed consensus algorithms especially for cases where the agents are subject to system failures.