Design of interaction in environmental load chain as connected directed network

In this paper, we propose control mechanism to reduce of environmental load as a stability model for connected directed network. The amount of change of environmental load is formulated as the global connected graph with a nonlinear mapping. The proposal technique can be utilized as signal control managing volume of environmental load. We first introduce feedback inputs that satisfy the Lyapunov asymptotically stable of total system with asymmetric connection. Furthermore we derive an equivalent transform from feedback inputs to adjustment of strength of interaction. In numerical examples, we show that our mechanism can control volume of environment to target state even if the network dynamics is under a complicated situation. The development technique is also possible to apply to multi-agent model, management of social system and so on.