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.

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.

In this work we address the problem of event-based data scheduling for multiple heterogeneous LTI control loops over a shared resource-constrained communication network. We introduce a novel bi-character scheduling scheme, which dynamically prioritizes the channel access at each time-step according to an error-dependent priority measure. Given local error thresholds for each control loop, the scheduling policy deterministically blocks the transmission from subsystems with lower error values. The scheduler then allocates the limited communication resource probabilistically among the eligible subsystems based on a prioritized measure. We prove stochastic stability of the networked control system under the proposed scheduler in terms of fergodicity of the overall network-induced error. Uniform analytical performance bounds are further derived for an average cost function comprised of a quadratic error term and transmission penalty. The simulation results show that our approach results in a significant reduction of the aggregate network-induced error variance compared to the conventional scheduling protocols.

In this paper, we study event-triggered data scheduling for stochastic multi-loop control systems communicating over a shared network with communication uncertainties. We introduce a novel dynamic scheduling scheme which allocates the channel access according to an error-dependent policy. The proposed scheduler deterministically excludes subsystems with lower error values from the medium access competition in favor of those with larger errors. Subsequently, the scheduler probabilistically allocates the communication resource to the eligible entities. We model the overall networkinduced error as a homogeneous Markov chain and show its boundedness in expectation over a multi time-step horizon. In addition, analytical upper bound for the associated average cost is derived. Furthermore, we show that our proposed policy is robust against packet dropouts. Numerical results demonstrate a significant performance improvement in terms of error level in comparison with periodic and random scheduling policies. 53rd IEEE Conference on Decision and Control

Control over shared communication networks is a key challenge in design and analysis of cyber-physical systems. The quality of control in such systems might be degraded due to the congestion while accessing the scarce communication resources. In this paper, we consider a multiple-loop networked control system (NCS), where all control loops share a communication network. Medium Access Control (MAC) is performed in contention-based fashion using a multi-channel slotted ALOHA protocol, where each control loop decides locally whether to attempt a transmission based on some error thresholds. We further introduce a local event-based resource-aware scheduling design with an adaptive choice of the error thresholds for a transmission. This leads to a hybrid channel access mechanism where the control loops are deterministically categorized into two sets of eligible and ineligible sub-systems for transmission in an event-based fashion, before a random process to select the available channels. In addition, employing the introduced policy, we show the stability of the resulting NCS in terms of Lyapunov stability in probability. We illustrate numerically the efficiency of our proposed approach in terms of reducing the average networked-induced error variance, and show the superiority of the adaptive event-based scheduler compared to the scheduling design with non-adaptive thresholds.

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Abstract-This paper modifies a recently proposed eventbased probabilistic medium access for multi-loop Networked Control Systems (NCSs) over a shared communication channel subject to limited capacity and uncertainties and study its robustness. The novel design combines deterministic and probabilistic attributes to efficiently allocate the channel access among the control loops in the presence of network-induced phenomena such as packet dropouts and scheduling with delayed information update. Since the scheduler receives error information from a number of systems simultaneously, this sheer amount of information cannot always be processed in timely manner, which in turn gives rise to delays. Given the local error thresholds, the subsystems with error values lower than their corresponding thresholds are deterministically excluded from the medium access competition in favor of those with larger errors. In case of resource scarcity, the scheduler probabilistically allocates the channel to those that exceed the local thresholds according to an error-dependent priority measure. We show stochastic stability of such NCSs in terms of f -ergodicity of the network-induced error, which is modeled as a Markov chain. Numerical results validate our stability results in the presence of packet dropouts and delayed data update.

In the design of closed-loop networked control systems (NCSs), induced transmission delay between sensors and the control station is an often-present issue which compromises control performance and may even cause instability. A very relevant scenario in which network-induced delay needs to be investigated is costly usage of communication resources. More precisely, advanced communication technologies, e.g. 5G, are capable of offering latency-varying information exchange for different prices. Therefore, induced delay becomes a decision variable. It is then the matter of decision maker's willingness to either pay the required cost to have low-latency access to the communication resource, or delay the access at a reduced price. In this article, we consider optimal price-based bi-variable decision making problem for single-loop NCS with a stochastic linear time-invariant system. Assuming that communication incurs cost such that transmission with shorter delay is more costly, a decision maker determines the switching strategy between communication links of different delays such that an optimal balance between the control performance and the communication cost is maintained. In this article, we show that, under mild assumptions on the available information for decision makers, the separation property holds between the optimal link selecting and control policies. As the cost function is decomposable, the optimal policies are efficiently computed.delay-dependent switching policies for a single-loop NCS with costly communication. The switching law determines the length of delay associated with the data sent over the network. We assume that every transmission incurs a cost determined by the associated delay, such that shorter delay incurs higher cost. Aggregating the LQG cost and delaydependent communication cost over a finite horizon, we derive the optimal control and switching laws assuming that communication prices are known apriori. It is then shown that the optimal control and switching laws are separable in expectation, and thus can be computed offline. It guarantees the computational feasibility of our proposed approach.