This article studies stochastic relative phase stability, i.e., stochastic phase-cohesiveness, of discrete-time phase-coupled oscillators. The stochastic phase-cohesiveness in two types of networks is studied. First, we consider oscillators coupled with 2π-periodic odd functions over underlying undirected graphs subject to both multiplicative and additive stochastic uncertainties. We prove stochastic phase-cohesiveness of the network with respect to two specific, namely, in-phase and antiphase, sets by deriving sufficient coupling conditions. We show the dependency of these conditions on the size of the mean values of additive and multiplicative uncertainties, as well as the sign of the mean values of multiplicative uncertainties. Furthermore, we discuss the results under a relaxation of the odd property of the coupling function. Second, we study an uncertain network in which the multiplicative uncertainties are governed by the Bernoulli process representing the well-known Erdös-Rényi network. We assume constant exogenous frequencies and derive sufficient conditions for achieving both stochastic phase-cohesive and phase-locked solutions, i.e., stochastic phase-cohesiveness with respect to the origin. For the latter case, where identical exogenous frequencies are assumed, we prove that any positive probability of connectivity leads to phase-locking. Thorough analyses are provided, and insights obtained from stochastic analysis are discussed, along with numerical simulations to validate the analytical results.

Consider a network of multiple independent stochas-tic linear systems where, for each system, a scheduler collocatedwith the sensors arbitrates data transmissions to a correspondingremote controller through a shared contention-based communi-cation network. While the systems are physically independent,their optimal controller design problems may, in general, becomecoupled, due to network contention, if the schedulers triggertransmissions based on state-dependent events. In this article wepropose a class of probabilistic admissible schedulers for whichthe optimal controllers, with respect to local standard LQG costs,have the certainty equivalence property and can still be determineddecentrally. Then, two subclasses of scheduling policies withinthis class are introduced; a non-event-based subclass, so calledpurely stochastic transmission (PST) policy, and an event-basedsubclass, both with easily adjustable triggering probabilities atevery time step. We then prove that, given a PST policy withgiven triggering probabilities and an associated closed-loop per-formance with optimal control law, we can find an event-basedscheduler from the proposed subclass and with the same trigger-ing probabilities for which the associated closed-loop performancewith optimal control law is strictly superior. Moreover, we showthat, for each closed-loop system, the optimal state estimatorsfor both scheduling policies follows a linear iteration. Finally, weprovide a method to regulate the triggering probabilities of theschedulers by maximizing a network utility function.

In the design of cyber-physical systems (CPS) where multiple physical systems are coupled via a communication network, a key aspect is to study how network services are distributed. In this letter, we first describe a cross-layer model for CPS to explicitly capture the coupling between control and networking and the time-sensitive requirements of each physical system. Physical systems processes are coupled via a shared network that provides a diverse range of cost-prone and capacity-limited services with distinct latency characteristics. Service prices are given such that low latency services incur higher communication cost, and prices remain fixed over a constant period of time but will be adjusted by the network for the future time periods. Physical systems decide to use specific services over each time interval depending on the service prices and their own time sensitivity requirements. Considering the service availability, the network coordinates resource allocation such that physical systems are serviced the closest to their preferences. Performance of individual systems are measured by an expected quadratic cost and we formulate a social optimization problem subject to time-sensitive requirements of the physical systems and the network constraints. From the formulated social optimization problem, we derive the joint optimal time-sensitive control and service allocation policies.

In the operation of networked control systems (NCSs), where multiple processes share a resource-limited and time-varying cost-sensitive network, communication delay is inevitable and primarily induced by, first, intermittent sensor sampling to restrict nonurgent transmissions, and second, resource management to avoid contentions, excessive traffic, and data loss. In a heterogeneous scenario, where control systems may tolerate only specific levels of sensor-to-controller latency, delay sensitivities need to be considered in the design of control and network policies to achieve the desired performance guarantees. We propose a cross-layer optimal co-design of control, sampling, and resource management policies for an NCS consisting of multiple stochastic linear time-invariant systems which close their sensor-to-controller links over a shared network. Aligned with advanced communication technology, we assume that the network offers a range of latency-varying transmission services for given prices. The performance of the local closed-loop systems is measured by a combination of linear-quadratic Gaussian cost and a suitable communication cost, and the overall objective is to minimize a defined social cost by all three policymakers. We derive optimal control, sampling, and resource allocation policies under different cross-layer awareness models, including constant and time-varying parameters, and show that higher awareness generally leads to performance enhancement at the expense of higher computational complexity. This trade-off is shown to be a key feature to select the proper interaction structure for the codesign.

This paper proposes an event-triggered add-on safety mechanism to adjust the control parameters for timely braking in a networked vehicular system while maintaining maneuverability. Passenger vehicle maneuverability is significantly affected by the combined slip friction effect, in which larger longitudinal tire slips result in considerable drop in lateral tire forces. This is of higher importance when unexpected dangerous situations occur on the road and immediate actions, such as braking, need to be taken to avoid collision. Harsh braking can lead to high-slip and loss of maneuverability; hence, timely braking is essential to reduce high-slip scenarios. In addition to the vehicles own active safety systems, the proposed event-triggered add-on safety is activated upon being informed about dangers by the road-side infrastructure. The aim is to incorporate the add-on safety feature to adjust the automatic control parameters for smooth and timely braking such that a collision is avoided while vehicle's maneuverability is maintained. We study two different wireless technologies for communication between the infrastructure and the vehicles, the Long-Term Evolution (LTE) and the fifth generation (5G) schemes. The safety advantages of the proposed framework is validated through high-fidelity software simulations. Copyright

Networked control system (NCS) refers to a set of control loops that are closed over a communication network. In this article, the joint operation of control and networking for NCS is investigated wherein the network serves the sensor-to-controller communication links for multiple stochastic linear time-invariant (LTI) subsystems. The sensors sample packets based on the observed plant state, which they send over a shared multihop network. The network has limited communication resources, which need to be assigned to competing links to support proper control loop operation. In this setup, we formulate an optimization problem to minimize the weighted-sum linear-quadratic-Gaussian cost of all loops, taking into account the admissible sampling, control, congestion control (CC), and scheduling policies. Under some mild assumptions on the sampling frequencies of the control loops and the communication network, we find the joint optimal solution to be given by a certainty equivalence control with a threshold-based sampling policy, as well as a back-pressure-type scheduler with a simple pass-through CC. The interface between network and control loops is identified to be the buffer state of the sensor node, which can be interpreted as network price for sampling a packet from the control perspective. We validate our theoretical claims by simulating NCSs comprised of multiple LTI stochastic control loops communicating over a two-hop cellular network.

In the design of multi-loop Networked Control Systems (NCSs), wherein each control system is characterized by heterogeneous dynamics and associated with a certain set of timing specifications, appropriate metrics need to be employed for the synthesis of control and networking policies to efficiently respond to the requirements of each control loop. The majority of the design approaches for sampling, scheduling, and control policies include either time-based or event-based metrics to perform pertinent actions in response to the changes of the parameters of interest. We specifically focus in this article on Age-of-Information (AoI) as a recently-developed time-based metric and threshold-based triggering function as a generic Event-Triggered (ET) metric. We consider multiple heterogeneous stochastic linear control systems that close their feedback loops over a shared communication network. We investigate the co-design across the NCS and discuss the pros and cons with the AoI and ET approaches in terms of asymptotic control performance measured by Linear-Quadratic Gaussian (LQG) cost functions. In particular, sampling and scheduling policies combining AoI and stochastic ET metrics are proposed. It is argued that pure AoI functions that generate decision variables solely upon minimizing the average age irrespective of control systems dynamics may not be able to improve the overall NCS performance even compared with purely randomized policies. Our theoretical analysis is validated through several simulation scenarios.

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.

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 letter, 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 letter, 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. 

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 non-negative and non-decreasing function of AoI. The parameters of this function include the LTI matrix and the covariance of exogenous noise in the LTI system. Noting that the formulated problem is a stochastic combinatorial optimization problem and is hard to solve, we resort to heuristic algorithms 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.