This paper introduces an analytical framework to investigate optimal design choices for the placement of virtual controllers along the cloud-to-things continuum. The main application scenarios include low-latency cyber-physical systems in which real-time control actions are required in response to the changes in states of an IoT node. In such cases, deploying controller software on a cloud server is often not tolerable due to delay from the network edge to the cloud. Hence, it is desirable to trade reliability with latency by moving controller logic closer to the network edge. Modeling the IoT node as a dynamical system that evolves linearly in time with quadratic penalty for state deviations, recursive expressions for the optimum control policy and the resulting minimum cost value are obtained by taking virtual fog controller reliability and response time latency into account. Our results indicate that latency is more critical than reliability in provisoning virtualized control services over fog endpoints, as it determines the swiftness of the fog control system as well as the timeliness of state measurements. Based on a realistic drone trajectory tracking model, an extensive simulation study is also performed to illustrate the influence of reliability and latency on the control of autonomous vehicles over fog.
On the side of control systems, the papers @cite_9 @cite_2 considered virtualized control services over the cloud. In @cite_6 , the author investigated an integrated play-back mechanism to improve the efficiency of remote control over the network. In @cite_37 , they studied the design of a physical control system over a wireless link that can corrupt transmitted data. These papers, however, do not employ any optimization framework to compute the structure of a virtual controller to be run at a fog endpoint. The papers @cite_51 @cite_25 @cite_45 @cite_24 , on the other hand, adopted a more optimization theory based approach to design control systems over communication channels either allowing opportunistic transmissions @cite_51 @cite_25 or dropping packets randomly @cite_15 @cite_24 . The main point of difference of the current paper from @cite_51 @cite_25 @cite_45 @cite_24 is that we focus on the virtual controller placement over fog by considering reliability and latency dimensions simultaneously. We show that the optimum virtual fog controller runs an estimator as a delay compensator, which does not appear in these papers. Further, the issue of reliability in our model is shifted from communication links to virtual fog controllers.
@cite_37 @cite_9 @cite_6 @cite_24 @cite_45 @cite_2 @cite_15 @cite_51 @cite_25
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In this paper, we consider a robust network control problem. We consider linear unstable and uncertain discrete time plants with a network between the sensor and controller and the controller and plant. We investigate the effect of data drop out in the form of packet losses. Four distinct control schemes are explored and sufficient conditions to ensure almost sure stability of the closed loop system are derived for each of them in terms of minimum packet arrival rate and the maximum uncertainty. I. INTRODUCTION In the past decade, networked control systems (NCS) have gained much attention from both the control com- munity and the network and communication community. When compared with classical feedback control system, networked control systems have several advantages. For example, they can reduce the system wiring, make the system easy to operate and maintain and later diagnose in case of malfunctioning, and increase system agility (20). Although NCS have advantages, inserting a network in between the plant and the controller introduces many problems as well. For instance, zero-delayed sensing and actuation, perfect information and synchronization are no longer guaranteed in the new system architecture as only finite bandwidth is available and data packet drops and delays may occur due to network traffic conditions. These must be revisited and analyzed before networked control systems become prevalent. Recently, many researchers have spent effort on these issues and some significant results were obtained and many are in progress. Many of the aforementioned issues are studied separately. Tatikonda (19) and Sahai (13) have presented some interesting results in the area of control under communication constraints. Specifically, Tatikonda gave a necessary and sufficient condition on the channel data rate such that a noiseless LTI system in the closed loop is asymptotically stable. He also gave rate results for stabilizing a noisy LTI system over a digital channel. Sahai proposed the notion of anytime capacity to deal with real time estimation and control for a networked control system. In our paper (17), the authors have considered various rate issues under finite bandwidth, packet drops and finite controls. An optimal bit allocation scheme is given in (16) under the networked setting. The effect of pacekt drops on state estimation was studied by Sinopoli, et. al. in (3). It has further been investigated by many researchers including the present authors in (15) and (6). Providing real-time cloud services to Vehicular Clients (VCs) must cope with delay and delay-jitter issues. Fog computing is an emerging paradigm that aims at distributing small-size self-powered data centers (e.g., Fog nodes) between remote Clouds and VCs, in order to deliver data-dissemination real-time services to the connected VCs. Motivated by these considerations, in this paper, we propose and test an energy-efficient adaptive resource scheduler for Networked Fog Centers (NetFCs). They operate at the edge of the vehicular network and are connected to the served VCs through Infrastructure-to-Vehicular (I2V) TCP IP-based single-hop mobile links. The goal is to exploit the locally measured states of the TCP IP connections, in order to maximize the overall communication-plus-computing energy efficiency, while meeting the application-induced hard QoS requirements on the minimum transmission rates, maximum delays and delay-jitters. The resulting energy-efficient scheduler jointly performs: (i) admission control of the input traffic to be processed by the NetFCs; (ii) minimum-energy dispatching of the admitted traffic; (iii) adaptive reconfiguration and consolidation of the Virtual Machines (VMs) hosted by the NetFCs; and, (iv) adaptive control of the traffic injected into the TCP IP mobile connections. The salient features of the proposed scheduler are that: (i) it is adaptive and admits distributed and scalable implementation; and, (ii) it is capable to provide hard QoS guarantees, in terms of minimum maximum instantaneous rates of the traffic delivered to the vehicular clients, instantaneous rate-jitters and total processing delays. Actual performance of the proposed scheduler in the presence of: (i) client mobility; (ii) wireless fading; and, (iii) reconfiguration and consolidation costs of the underlying NetFCs, is numerically tested and compared against the corresponding ones of some state-of-the-art schedulers, under both synthetically generated and measured real-world workload traces. Wireless vehicle-to-vehicle (V2V) and vehicle-toinfrastructure (V2I) communication holds great promise for significantly reducing the human and financial costs of vehicle collisions. A common characteristic of this communication is the broadcast of a device's core state information at regular intervals (e.g., vehicle speed and location or traffic signal state and timing). Unless controlled, the aggregate of these broadcasts will congest the channel under dense traffic scenarios, reducing the effectiveness of collision avoidance applications that use transmitted information. Active congestion control using distributed techniques is a topic of great interest for establishing the scalability of this technology. This paper defines a new adaptive congestion control algorithm that can be applied to the message rate of devices in this vehicular environment. While other published approaches rely on binary control, the LInear MEssage Rate Integrated Control (LIMERIC) algorithm takes advantage of full-precision control inputs that are available on the wireless channel. The result is provable convergence to fair and efficient channel utilization in the deterministic environment, under simple criteria for setting adaptive parameters. This “perfect” convergence avoids the limit cycle behavior that is inherent to binary control. We also discuss several practical aspects associated with implementing LIMERIC, including guidelines for the choice of system parameters to obtain desired utilization outcomes, a gain saturation technique that maintains robust convergence under all conditions, convergence with asynchronous updates, and using channel load to determine the aggregate message rate that is observable at a receiver. This paper also extends the convergence analysis for two important cases, i.e., measurement noise in the input signal and delay in the update process. This paper illustrates key analytical results using MATLAB numerical results and employs standard NS-2 simulations to demonstrate the performance of LIMERIC in several high-density scenarios. Distributed processing through ad hoc and sensor networks is having a major impact on scale and applications of computing. The creation of new cyber-physical services based on wireless sensor devices relies heavily on how well communication protocols can be adapted and optimized to meet quality constraints under limited energy resources. The IEEE 802.15.4 medium access control protocol for wireless sensor networks can support energy efficient, reliable, and timely packet transmission by a parallel and distributed tuning of the medium access control parameters. Such a tuning is difficult, because simple and accurate models of the influence of these parameters on the probability of successful packet transmission, packet delay, and energy consumption are not available. Moreover, it is not clear how to adapt the parameters to the changes of the network and traffic regimes by algorithms that can run on resource-constrained devices. In this paper, a Markov chain is proposed to model these relations by simple expressions without giving up the accuracy. In contrast to previous work, the presence of limited number of retransmissions, acknowledgments, unsaturated traffic, packet size, and packet copying delay due to hardware limitations is accounted for. The model is then used to derive a distributed adaptive algorithm for minimizing the power consumption while guaranteeing a given successful packet reception probability and delay constraints in the packet transmission. The algorithm does not require any modification of the IEEE 802.15.4 medium access control and can be easily implemented on network devices. The algorithm has been experimentally implemented and evaluated on a testbed with off-the-shelf wireless sensor devices. Experimental results show that the analysis is accurate, that the proposed algorithm satisfies reliability and delay constraints, and that the approach reduces the energy consumption of the network under both stationary and transient conditions. Specifically, even if the number of devices and traffic configuration change sharply, the proposed parallel and distributed algorithm allows the system to operate close to its optimal state by estimating the busy channel and channel access probabilities. Furthermore, results indicate that the protocol reacts promptly to errors in the estimation of the number of devices and in the traffic load that can appear due to device mobility. It is also shown that the effect of imperfect channel and carrier sensing on system performance heavily depends on the traffic load and limited range of the protocol parameters.