Performance Characterization Using AoI in a Single-loop Networked Control System
Jaya Prakash Champati, Mohammad H. Mamduhi, Karl H. Johansson, James Gross
TL;DR
This paper studies a single-loop Networked Control System with i.i.d. transmission delays and an event-based sampler, aiming to minimize the time-average squared estimation error. It proves that, under mild information-structure assumptions, the optimal control law can be taken as certainty-equivalent and independent of the sampling policy, and that the estimation error cost can be expressed as a function of AoI when sampling decisions do not depend on the plant state; this yields an AoI-based reformulation $\mathbb{E}[f(\Delta)]$ with $f(\Delta) = \sum_{i=0}^{\Delta-1} \textsf{Tr}(A^{i^\top} A^{i} \Sigma)$. The authors introduce heuristics, notably MEAS, to minimize $\mathbb{E}[f(\Delta)]$ by computing waiting times $G_k$ from the previous transmission time via $g(y) = \max(\beta - y, 0)$ with $\beta$ solved from $\mathbb{E}[(Y+g(Y))^2] = 2\beta \mathbb{E}[Y+g(Y)]$, and analyze a corollary where minimizing $\mathbb{E}[f(\Delta)]$ reduces to minimizing $\mathbb{E}[\Delta]$ for certain $A$ (e.g., orthogonal). Numerical results under geometric service times show MEAS can outperform or closely match a low-complexity zero-wait baseline, with the latter performing particularly well when $A=1$ but diverging for $A>1$. Overall, the work links AoI-based scheduling with control performance, offering practical AoI-driven design methods for NCSs and directions for future research.
Abstract
The joint design of control and communication scheduling in a Networked Control System (NCS) is known to be a hard problem. Several research works have successfully designed optimal sampling and/or control strategies under simplified communication models, where transmission delays/times are negligible or fixed. However, considering sophisticated communication models, with random transmission times, result in highly coupled and difficult-to-solve optimal design problems due to the parameter inter-dependencies between estimation/control and communication layers. To tackle this problem, in this work, we investigate the applicability of Age-of-Information (AoI) for solving control/estimation problems in an NCS under i.i.d. transmission times. Our motivation for this investigation stems from the following facts: 1) recent results indicate that AoI can be tackled under relatively sophisticated communication models, and 2) a lower AoI in an NCS may result in a lower estimation/control cost. We study a joint optimization of sampling and scheduling for a single-loop stochastic LTI networked system with the objective of minimizing the time-average squared norm of the estimation error. We first show that under mild assumptions on information structure the optimal control policy can be designed independently from the sampling and scheduling policies. We then derive a key result that minimizing the estimation error is equivalent to minimizing a function of AoI when the sampling decisions are independent of the state of the LTI system. Noting that minimizing the function of AoI is a stochastic combinatorial optimization problem and is hard to solve, we resort to heuristic algorithms obtained by extending existing algorithms in the AoI literature. We also identify a class of LTI system dynamics for which minimizing the estimation error is equivalent to minimizing the expected AoI.