Stochastic Control with Stale Information--Part I: Fully Observable Systems

TL;DR

This paper investigates the impact of information staleness on stochastic control systems, identifying fundamental limits and optimal policies for stabilization under stale information conditions.

Contribution

It introduces a framework linking information age to control performance, deriving optimal control and queuing policies for systems with stale data.

Findings

Identifies a critical staleness threshold for stabilization.

Formulates the problem as a stochastic optimization.

Derives optimal control and queuing policies.

Abstract

In this study, we adopt age of information as a measure of the staleness of information, and take initial steps towards analyzing the control performance of stochastic systems with stale information. Our goals are to cast light on a fundamental limit on the information staleness that is required for a certain level of the control performance and to specify the corresponding stalest information pattern. In the asymptotic regime, such a limit asserts a critical information staleness that is required for stabilization. We achieve these goals by formulating the problem as a stochastic optimization problem and characterizing the associated optimal solutions. These solutions are in fact a control policy, which specifies the control inputs of the plant, and a queuing policy, which specifies the staleness of information at the controller.