This paper investigates the remote state estimation for a cyber–physical system (CPS) where a group of (primary) sensors transmit sensing data packets to the remote estimators for state estimation via their individual channels. In view of the complexity arising from the scale of such system, it is desirable for the primary sensors to share their channels with the newly-added (potential) ones, especially when the sensing data of primary ones contains less valuable information. However, the channel sharing inevitably leads to signal interference among sensors using the same channels, and it may further degenerate the remote estimation performance. Thus, the system designer should allocate the transmission power for sensors to maximize the global estimation accuracy. We emphasize the noncooperative nature among sensors, and solve the problem in an exchange market framework with a platform acting on behalf of the system designer, and prove that the optimal power allocation is a spontaneous outcome of the market under well-designed prices. More specifically, under (subsidized) prices announced by the platform, the primary sensors are willing to open up their channels for sharing, in which a distributed optimal power allocation is derived explicitly. To alleviate transmission interference, the platform will charge potential sensors for the use of channels, among which the mutual interaction is formulated as a non-cooperative game and the existence of a pure Nash equilibrium is proved. We also devise an algorithm for the platform to design subsidized/toll prices, which is given in an explicit recursive form with simple iterations, and therefore suited for the platform with limited computation capability. Publication: - Automatica, 129 (2021). Authors: - Kemi Ding (Hong Kong University of Science and Technology) - Xiaoqiang Ren (Shanghai University) - Hongsheng Qi (Institute of Systems Science, AMSS, Chinese Academy of Sciences) - Guodong Shi (The University of Sydney) - Xiaofan Wang (Shanghai University) - Ling Shi (Hong Kong University of Science and Technology)
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