Fast-and-Secure State-Estimation in Dynamic-Control Over Communication Channels: A Game-Theoretical Viewpoint

“Control over noisy communication-channels” invented by Sahai-Mitter-and-Tatikonda is a prominent topic. In this context, the latency-and-reliability trade-off is considered by responding to the following: How much fast? How much secure? For a stochastic-mean-field-game (S-MFG), we assign the source-codes as the agents. Additionally, the total-Reward is the Volume of the maximum secure lossy source-coding-rate achievable between a set of Sensors, and the Fusion-Centre (FC) set - including intercepting-Byzantines. The total-Reward is guaranteed by a set of private Helpers. We consider 2 cases for the population in our game: (i) the finite-games-partially-sufficiently-many-agents (FG-PSuMA) case in-accordance with finite-blocklength which causes us to experience ε-equilibria; and (ii) the infinite-games-infinite-agents (IG-IA) case in-correspondence to the Mean-Field-Limit issue. Consequently, we evaluate the steady-state of our S-MFG via a time-varying graph while evaluating the stabilisability through the principles of the Kolmogorov-Distance (K-D) and Nyquist. A novel calculation for the information-flux over the Riemannian-Manifold is also proposed by translating the wavy-wall boundary-conditions. Finally, the correctness of our novelties is evaluated.