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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This article includes an implementation of an 802.11b wireless control loop with high communication rates and a timing scheme that uses clock driven sensing and actuation with event-driven control. The timing scheme was implemented using standard PCs and an 802.11b peer-to-peer wireless network. The control scheme was scaled up to a multimode multiplant arrangement with coordination among loops. To examine the wireless control loop performance, we use the rotating base variation of the linear inverted pendulum. Using the wireless control loop, we can examine a number of the characteristics of UDP data transmission over 802.11b. Event-based control has gained significant interest from the research community in recent years because it allows better resource utilization in networked control systems. In this paper, we propose an architecture for offering event-based control as a service from the cloud, which not only improves resource utilization but also reduces the cost and setup time of large-scale industrial automation systems. Providing event-based control from the cloud, however, poses multiple research challenges. We address two of the main challenges, which are the network delays and failures introduced because of moving the controller far away from the plant. We present a delay mitigation technique that maintains the stability and performance of the control system. Our results using commercial clouds show that our delay mitigation technique can handle large communication delays up to several seconds with practically zero effect on the main performance metrics of the system. Moreover, our proposed fault tolerance approach can effectively handle network failures even if the controlled system is thousands of miles away from its cloud controllers. Sensing, actuation, and decision units can control a remote physical environment and enable physical actions regardless of distance. However, the effectiveness of networked control depends on its ability to tolerate network non-determinism, which in turn can be enhanced by the use of play-back buffers. Although play-back has been intensively studied in multi-media applications, play-back schemes differ significantly in networked control, which is characterized by different performance metrics and a different sequence of communication events. The primary contribution of this paper is an end-to-end algorithm that integrates play-back buffering, sensor sampling, and control. The algorithm is extensively validated on simulations and realtime wide-area emulations. The integrated algorithm canceled the effect of disturbances as much as a proportional controller under ideal network conditions. In this paper, optimal control of linear time-invariant (LTI) systems over unreliable communication links is studied. The motivation of the problem comes from growing applications that demand remote control of objects over Internet-type or wireless networks where links are prone to failure. Depending on the availability of acknowledgment (ACK) signals, two different types of networking protocols are considered. Under a TCP structure, existence of ACK signals is assumed, unlike the UDP structure where no ACK packets are present. The objective here is to mean-square (m.s.) stabilize the system while minimizing a quadratic performance criterion when the information flow between the controller and the plant is disrupted due to link failures, or packet losses. Sufficient conditions for the existence of stabilizing optimal controllers are derived. We consider multiple sensors randomly accessing a shared wireless medium to transmit measurements of their respective plants to a controller. To mitigate the packet collisions arising from simultaneously transmitting sensors, we appropriately design the sensor access rates. This is posed as an optimization problem, where the total transmit power of the sensors is minimized, and control performance for all control loops needs to be guaranteed. Control performance of each loop is abstracted as a desired expected decrease rate of a given Lyapunov function. By establishing an equivalent convex optimization problem, the optimal access rates are shown to decouple among sensors. Moreover, based on the Lagrange dual problem, we develop an easily implementable distributed procedure to find the optimal sensor access rates.