Design of State-based Schedulers for a Network of Control Loops

TL;DR

This paper proposes a state-based scheduler for networked control systems that optimizes packet transmission under network contention, ensuring separation of scheduling, estimation, and control for improved system performance.

Contribution

It introduces a dual predictor architecture with certainty equivalence, simplifying the design of schedulers and controllers in networked control loops with contention-based access.

Findings

Certainty equivalence holds when past controls are removed from scheduling criteria.

A dual predictor architecture ensures separation between scheduler, observer, and controller.

The proposed network-aware event-triggering mechanism improves packet selection under traffic conditions.

Abstract

For a closed-loop system, which has a contention-based multiple access network on its sensor link, the Medium Access Controller (MAC) may discard some packets when the traffic on the link is high. We use a local state-based scheduler to select a few critical data packets to send to the MAC. In this paper, we analyze the impact of such a scheduler on the closed-loop system in the presence of traffic, and show that there is a dual effect with state-based scheduling. In general, this makes the optimal scheduler and controller hard to find. However, by removing past controls from the scheduling criterion, we find that certainty equivalence holds. This condition is related to the classical result of Bar-Shalom and Tse, and it leads to the design of a scheduler with a certainty equivalent controller. This design, however, does not result in an equivalent system to the original problem, in the sense of Witsenhausen. Computing the estimate is difficult, but can be simplified by introducing a symmetry constraint on the scheduler. Based on these findings, we propose a dual predictor architecture for the closed-loop system, which ensures separation between scheduler, observer and controller. We present an example of this architecture, which illustrates a network-aware event-triggering mechanism.