An algorithm with low computational requirements to constrain the Shapley value in coalitional networks

Abstract

In this paper, we deal with a distributed control scheme for linear systems in which the local controllers work cooperatively whenever the benefits from a control perspective are higher than the corresponding communication requirements. To this end, the network topology may vary with time so that all the communication links with a minor contribution to the overall performance are disconnected. Hence, there is also a change in the overall control law, which must be adapted to the information flows enabled by the network topology. This whole framework can be modeled as a cooperative game, which allows us to apply tools such as the Shapley value to gain an insight into the distributed control problem. In particular, we show an alternative way to impose restrictions on this value by using a more computationally efficient design procedure.