Energy-Efficient Co-Design of Power Scheduling for State Estimation Over a Stochastic Delayed Network

In this article, the scheduling problem over a delayed network is investigated. Different from the existing literature, we propose a hybrid stochastic model which incorporates both delay and packet loss. Based on this proposed model, an energy-efficient co-design problem is considered under power-limited scenarios. A global optimal offline solution is presented explicitly. Aided by arriving information feedback, we propose an online schedule based on an absolute threshold. The optimality of our proposed schemes and thresholds selection is theoretically analyzed. Meanwhile, we have extended the conclusions of the single-system case to the multisystem case. Optimal strategies from both offline and online perspectives are provided with rigorous proof, respectively. The stability condition is given for the estimator to converge in an infinite-time horizon. The comparisons between offline and online strategies are proved the global superiority of the online strategy to the offline one. Numerical simulations have validated the correctness and superiority of our proposed algorithms.