Distributed Value of Information in Feedback Control over Multi-hop Networks

Abstract: Recent works in the domain of networked control systems have demonstrated that the joint design of medium access control strategies and control strategies for the closed-loop system is beneficial. However, several metrics introduced so far fail in either appropriately representing the network requirements or in capturing how valuable the data is. In this paper we propose a distributed value of information (dVoI) metric for the joint design of control and schedulers for medium access in a multi-loop system and multi-hop network. We start by providing conditions under certainty equivalent controller is optimal. Then we reformulate the joint control and communication problem as a Bellman-like equation. The corresponding dynamic programming problem is solved in a distributed fashion by the proposed VoI-based scheduling policies for the multi-loop multi-hop networked control system, which outperforms the well-known time-triggered periodic sampling policies. Additionally we show that the dVoI-based scheduling policies are independent of each other, both loop-wise and hop-wise. At last, we illustrate the results with a numerical example.