AoI-Penalty Minimization for Networked Control Systems with Packet Loss

Abstract

In this work the impact of age of information (AoI) is studied from the perspective of networked control systems (NCS), i.e., control loops that are closed over networks. We formulate the estimation problem of a linear time invariant (LTI) system and show that related performance metrics can be optimized by minimizing age-penalty functions. From the variety of possible penalties that make sense from an NCS point of view, we derive a general age-penalty minimization problem. We characterize properties of penalty functions that are trivial or non-trivial to solve and show that for non-trivial age-penalties, the optimal transmission policy over a single link with packet loss is AoI-threshold based. Then, we propose an algorithm to find the optimal threshold. Simulation results verify that threshold policies with optimal threshold can serve to optimally solve a variety of NCS related estimation problems.

Sampling for data freshness optimization: Non-linear age functions

“…The above result can be generalized to the state estimation error of feedback control systems [18], [19]. Consider a singleloop feedback control system, where a plant and a controller are governed by a Linear Time-Invariant (LTI) system, i.e.,…”

“…In this paper, we suggest to use a non-linear function u(∆ t ) of the age ∆ t as a data freshness metric, where u(∆ t ) could be the utility value of data with age ∆ t , temporal autocorrelation function of the source, estimation error of signal value, or other application-specific performance metrics [1], [5]- [19]. A survey of non-linear age functions and their applications is provided in Section III-B.…”

A Whittle Index Approach to Minimizing Functions of Age of Information

“…Observe that we assumed f (·) to be non-decreasing. This combined with (21) and the Bellman equations (16) and (18) ensures that S(·) is also non-decreasing. Thus, if there exists a state H that satisfies (20), then the threshold policy with threshold H satisfies the Bellman equations and is hence optimal.…”

“…Nonlinear functions of age have also been discussed in the context of networked control systems in [17], [18] and [19]. In [17], the authors discuss a real time networked control system and show that the cost function is characterized as a nondecreasing, possibly nonlinear, function of AoI.…”

“…In [17], the authors discuss a real time networked control system and show that the cost function is characterized as a nondecreasing, possibly nonlinear, function of AoI. In [18], the authors formulated the state estimation problem for an LTI system, where the state of a discrete-time LTI system can be observed in any time-slot by paying a fixed transmission cost. The problem of minimizing the time-average of the sum of the estimation error and transmission cost reduces to minimizing a non-decreasing age-cost function for a single source with a fixed transmission cost.…”