Consensus problems on networks with free protocol

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In the real world,rule makers can only restrict,not completely control the behavior of the governed,while the gov-erned can only choose their behavior patterns under these restrictions.In this paper,we design a new control protocol called free protocol to describe this situation.First,we calculate consensus probabilities based on the information of the interaction networks.Then,sufficient conditions are obtained for all agents converging to a same value with probability one.Finally,numerical simulation results are given to verify the above results.
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