Network entropy and data rates required for networked control

TL;DR

This paper introduces the concept of subsystem invariance entropy to quantify the minimum data rates needed for networked control systems to achieve state invariance, analyzing trade-offs and optimal data rate configurations.

Contribution

It defines subsystem invariance entropy and characterizes the Pareto-optimal data rates for linear systems and chaos synchronization, advancing understanding of data rate constraints in networked control.

Findings

Subsystem invariance entropy quantifies minimal data rates for control.

A convex set of data rate combinations guarantees control objectives.

Pareto-optimal data rate points reveal trade-offs in network control.

Abstract

We consider the problem of making a set of states invariant for a network of controlled systems. We assume that the subsystems, initially uncoupled, must be interconnected through controllers to be designed with a constraint on the data rate obtained by every subsystem from all the other subsystems. We introduce the notion of subsystem invariance entropy, which is a measure for the smallest data rate arriving at a fixed subsystem, above which the overall system is able to achieve the control goal. Moreover, we associate to a network of n subsystems a closed convex set of R^n encompassing all possible combinations of data rates within the network that guarantee the existence of corresponding feedback strategies for making a given set invariant. The extremal points of this convex set can be regarded as Pareto-optimal data rates for the control problem, expressing a trade-off between the data rates required by different systems. We characterize these quantities for linear systems, and for synchronization of chaos.