Distributed filtering with time-varying topology: A temporal-difference learning approach in dual games

This study aims to develop a dual games (DGs) mechanism and implement a temporal difference learning (TDL) approach to address distributed filter design while considering network-induced time-varying topology from individual optimality and global equilibrium perspectives. In a detailed analysis, each filtering node (FN) treats its individual filtering action and exogenous disturbance as opposing elements, striving to determine the optimal policy while accounting for the worst-case scenario. This competition between FN and the disturbance culminates in a zero-sum game. Simultaneously, FN collaborates effectively with its neighbors to achieve consensus estimation, giving rise to a non-zero-sum game. Notably, an error-based filtering action is built to solve challenges posed by DGs. Ultimately, each FN attains its estimation at a minimum cost, and the entire distributed filtering network achieves the consensus estimation at a Nash equilibrium. Moreover, the transition probability correlation matrices (TPCMs) of the time-varying topology are obtained through direct observation of multi-episodes of topological transition trajectories. It has been proved that with a sufficiently ample number of episodes, TPCMs converge to their optimal values when TPs are known as apriori. Finally, a numerical example and an aero-engine system are presented to illustrate the effectiveness and practical potential of the proposed method.