Privacy-based cooperation for networked cyber-physcial systems

This paper studies the privacy preserving problem for a group of reciprocity nodes, where the communication topology contains a directed spanning tree. A privacy-based cooperation protocol, in which Gaussian random variables are partly added, is elegantly proposed with the aim of protcting the information among interaction agents from malicious attackers. We then derive the minimum mean square error covariance matrix (MMSE-CM). It shows that privacy preserving problem is solved whenever the bounded MMSE-CM exceeds a predetermined threshold value. Of relevance to the recent results in the literature, the primary difficulties lie in that not only the restriction on the MMSE-CM should be larger than a priori given critical value, but also the amount of the added noise is as less as possible such that the cost of configuration or maintenance can meet a desire level, which is of practical importance. The state of the art is significantly strengthened when compared with some of the existing results in the literature.