Constraints on the shapley value for a coalitional control system

We introduce several refinements in the design method of a coalitional control scheme for linear systems recently proposed. In this scheme, the network topology is modified in order to attain a trade-off between communication burden and overall system performance. In particular, all the communication links with low contribution to the overall performance are disconnected. Likewise, the control law is adapted to these changes. Given that the coalitional control scheme can be described as a cooperative game, it is possible to apply classical game theory results to gain insight into the distributed control problem. In this work, we show how the design method can be modified in order to include constraints regarding the game theoretical properties of the aforementioned scheme.