AbstractWe consider a stochastic system where the communication between the controller and the actuatoris triggered by a threshold-based rule. The communication is performed across an unreliable link thatstochastically erases transmitted packets. To decrease the communication burden, and as a partial pro-tection against dropped packets, the controller sends a sequence of control commands to the actuator ineach packet. These commands are stored in a buffer and applied sequentially until the next control packetarrives. In this context, we study dead-beat control laws and compute the expected linear-quadratic loss ofthe closed-loop system for any given event-threshold. Furthermore, we provide analytical expressions thatquantify the trade-off between the communication cost and the control performance of event-triggeredcontrol systems. Numerical examples demonstrate the effectiveness of the proposed framework.Index TermsEvent-triggering algorithms; Linear systems; Communication networks; Packet loss; Networkedcontrol
The analysis becomes even more involved when the network is unreliable. Blind and Allg " o wer @cite_4 extended the work of @cite_27 to the case where transmissions from the sensor to the controller take place over an unreliable link. They analytically derived the control cost and the expected inter-event times for different packet loss rates. Rabi and Johansson @cite_36 designed the optimal impulse control and the level triggering mechanism under packet losses with multiple loops sharing a common network. From a different perspective, @cite_6 analyzed the stability of an event-triggered implementation of a controller in the presence of packet losses and limited processing resources. However, in all these works, the unreliable channel appears between sensor and controller, while the controller-actuator communication is lossless.
@cite_36 @cite_27 @cite_4 @cite_6
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For a single control loop with communication rate constraints, Event-triggered control often outperforms periodic control. When multiple loops are being controlled over a shared contention-based medium, however, the advantage of event-triggered policies is less well understood. In this paper, we consider event-triggered impulse control under lossy communication. The sampling events are determined by level crossings of the plant output. It is shown how a stochastic control criterion depends on the level thresholds and the packet loss probability for a class of integrator plants. For multiple control loops, this result is used to derive a design guideline on how to assign the levels that lead to optimal use of the available communication resources. It is shown that the structure of the event generator depends critically on the loss probability. In this work, we analyze event-based control for scalar systems with an impulsive input that resets the state to the origin when applied. The event information is transmitted within packets, which are randomly dropped. We derive the cost as well as the expected times between events and discuss how to change the bounds, which generate the events, after a packet loss. 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. This paper is concerned with the analysis, design and validation of a reliable management strategy for industrial monitoring and control over wireless sensor network (WSN). First, we investigate the interactions between contention resolution and congestion control mechanisms in Wireless Industrial Sensor Network (briefly WISN). An extensive set of simulations are performed in order to quantify the impacts of several network parameters (i.e. buffer, sensors reporting rate) on the overall network performance (i.e. reliability, packet losses). This calls for cross-layer mechanisms for efficient data delivery over WISN. Second, a reliable sink resource allocation strategy based on log-utility fairness criteria is proposed. It is shown that the resource sink manager can plan strategies to better allocate the available resource among competing sensors. Finally, the analysis, design and validation of a reliable sinks cooperative control for WISN are introduced. A sufficient condition for wireless network stability in presence of multiple sinks and heterogeneous sensors with different time delays is given and it is used for network parameters design. The stability condition and the resulting cooperative control performance in terms of fairness, link utilization, packet losses, reliability and latency are validated by Matlab Simulink-based simulator TrueTime, which facilitates co-simulation of controller task execution in real-time kernels and in the wireless network environment. Copyright © 2009 John Wiley & Sons, Ltd. Recent developments in computer and communication technologies have led to a new type of large-scale resource-constrained wireless embedded control systems. It is desirable in these systems to limit the sensor and control computation and or communication to instances when the system needs attention. However, classical sampled-data control is based on performing sensing and actuation periodically rather than when the system needs attention. This paper provides an introduction to event- and self-triggered control systems where sensing and actuation is performed when needed. Event-triggered control is reactive and generates sensor sampling and control actuation when, for instance, the plant state deviates more than a certain threshold from a desired value. Self-triggered control, on the other hand, is proactive and computes the next sampling or actuation instance ahead of time. The basics of these control strategies are introduced together with a discussion on the differences between state feedback and output feedback for event-triggered control. It is also shown how event- and self-triggered control can be implemented using existing wireless communication technology. Some applications to wireless control in process industry are discussed as well. We investigate control of a non-linear process when communication and processing capabilities are limited. The sensor communicates with the controller node through an erasure channel which introduces independent and identically distributed (i.i.d.) packet dropouts. Processor availability for control is random and, at times, insufficient to calculate plant inputs. To make efficient use of communication and processing resources, the sensor transmits only when the plant state lies outside a bounded target set. Control calculations are triggered by the received data. If a plant state measurement is successfully received and while the processor is available for control, the algorithm recursively calculates a sequence of tentative plant inputs, which are stored in a buffer for potential future use. This safeguards for time-steps when the processor is unavailable for control. We derive sufficient conditions on system parameters for stochastic stability of the closed loop and illustrate performance gains through numerical studies. 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). Networked control systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. We review several recent results on estimation, analysis, and controller synthesis for NCSs. The results surveyed address channel limitations in terms of packet-rates, sampling, network delay, and packet dropouts. The results are presented in a tutorial fashion, comparing alternative methodologies A fluid model of multi-class flows with priority packet scheduling is considered for controlling the flow rates, their end-to-end delays and their packet losses. We derive a globally stable distributed rate and delay combined control when no information time lags are present. By properly sizing the router buffers, the stable rates attain the end-to- end delay requirements without any packet loss. By further enhancing the network with bandwidth reservation and admission control, we also show that minimum rate is guaranteed. The stability properties of the discrete time version of our control are also derived when no information time lags are present. The stability in the presence of information time lags is studied numerically by computing the delay and rate trajectories for a real test-bed network. YouTube traffic is bursty. These bursts trigger packet losses and stress router queues, causing TCP's congestion-control algorithm to kick in. In this paper, we introduce Trickle, a server-side mechanism that uses TCP to rate limit YouTube video streaming. Trickle paces the video stream by placing an upper bound on TCP's congestion window as a function of the streaming rate and the round-trip time. We evaluated Trickle on YouTube production data centers in Europe and India and analyzed its impact on losses, bandwidth, RTT, and video buffer under-run events. The results show that Trickle reduces the average TCP loss rate by up to 43 and the average RTT by up to 28 while maintaining the streaming rate requested by the application. We introduce an event driven communication logic for decentralized control of a network of robotic vehicles (agents). The strategy proposed is robust to packet losses and drives the vehicles to predefined paths while holding a desired geometric formation pattern. To this effect, the paper extends an existing cooperative path following framework to consider the practical case where communications among the vehicles occur at discrete instants, instead of continuously. The introduced communication logic takes into account the topology of the communication network, the fact that communications are discrete, and the cost of exchanging information. We also address explicitly communication losses and bounded delays. Conditions are derived under which the overall closed loop system is input-to-state practically stable. The communication logic is applied to a cooperative path-following control system of multiple underactuated autonomous marine robots. Simulation results are presented and discussed. Cyber-Physical Systems (CPSs) resulting from the interconnection of computational, communication, and control (cyber) devices with physical processes are wide spreading in our society. In several CPS applications it is crucial to minimize the communication burden, while still providing desirable closed-loop control properties. To this effect, a promising approach is to embrace the recently proposed event-triggered control paradigm, in which the transmission times are chosen based on well-defined events, using state information. However, few general event-triggered control methods guarantee closed-loop improvements over traditional periodic transmission strategies. Here, we provide a new class of event-triggered controllers for linear systems which guarantee better quadratic performance than traditional periodic time-triggered control using the same average transmission rate. In particular, our main results explicitly quantify the obtained performance improvements for quadratic average cost problems. The proposed controllers are inspired by rollout ideas in the context of dynamic programming. Experimental studies have demonstrated that the behavior of real links in low-power wireless networks (such as wireless sensor networks) deviates to a large extent from the ideal binary model used in several simulation studies. In particular, there is a large transitional region in wireless link quality that is characterized by significant levels of unreliability and asymmetry, significantly impacting the performance of higher-layer protocols. We provide a comprehensive analysis of the root causes of unreliability and asymmetry. In particular, we derive expressions for the distribution, expectation, and variance of the packet reception rate as a function of distance, as well as for the location and extent of the transitional region. These expressions incorporate important environmental and radio parameters such as the path loss exponent and shadowing variance of the channel, and the modulation, encoding, and hardware variance of the radios. 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. Vehicular ad hoc networks play a critical role in enabling important active safety applications such as cooperative collision warning. These active safety applications rely on continuous broadcast of self-information by all vehicles, which allows each vehicle to track all its neighboring cars in real time. The most pressing challenge in such safety-driven communication is to maintain acceptable tracking accuracy while avoiding congestion in the shared channel. In this article we propose a transmission control protocol that adapts communication rate and power based on the dynamics of a vehicular network and safety-driven tracking process. The proposed solution uses a closed-loop control concept and accounts for wireless channel unreliability. Simulation results confirm that if packet generation rate and associated transmission power for safety messages are adjusted in an on-demand and adaptive fashion, robust tracking is possible under various traffic conditions. Current distributed routing paradigms (such as link-state, distance-vector, and path-vector) involve a convergence process consisting of an iterative exploration of intermediate routes triggered by certain events such as link failures. The convergence process increases router load, introduces outages and transient loops, and slows reaction to failures. We propose a new routing paradigm where the goal is not to reduce the convergence times but rather to eliminate the convergence process completely. To this end, we propose a technique called Failure-Carrying Packets (FCP) that allows data packets to autonomously discover a working path without requiring completely up-to-date state in routers. Our simulations, performed using real-world failure traces and Rocketfuel topologies, show that: (a) the overhead of FCP is very low, (b) unlike traditional link-state routing (such as OSPF), FCP can provide both low loss-rate as well as low control overhead, (c) compared to prior work in backup path pre-computations, FCP provides better routing guarantees under failures despite maintaining lesser state at the routers. 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. An event-triggered control technique for consensus of multi-agent systems with general linear dynamics is presented. This paper extends previous work to consider agents that are connected using directed graphs. Additionally, the approach shown here provides asymptotic consensus with guaranteed positive inter-event time intervals. This event-triggered control method is also used in the case where communication delays are present. For the communication delay case we also show that the agents achieve consensus asymptotically and that, for every agent, the time intervals between consecutive transmissions is lower-bounded by a positive constant. Measurements of LAN and WAN traffic show that network traffic exhibits variability on different scales. We examine a mechanism that gives rise to self-similar network traffic and discuss performance. The mechanism we study is the transfer of files or messages whose size is drawn from a heavy-tailed distribution. In a realistic client server network the degree to which file sizes are heavy-tailed can directly determine the degree of traffic self-similarity at the link level. This causal relationship is robust relative to changes in network resources, network topology, the influence of cross-traffic, and the distribution of interarrival times. Properties of the transport layer play an important role in preserving and modulating this relationship. The reliable transmission and flow control mechanisms of TCP serve to maintain the long-range dependency structure induced by heavy-tailed file size distributions. In contrast, if a non-flow-controlled and unreliable (UDP-based) transport protocol is used, the resulting traffic shows little self-similarity: although still bursty at short time scales, it has little long-range dependence. Performance implications of self-similarity are discussed as represented by various performance measures. Increased self-similarity as expected, results in degradation of performance. Queueing delay, in particular is discussed. Throughput-related measures such as packet loss and retransmission rate, however increase only gradually with increasing traffic self-similarity as long as reliable, flow-controlled transport protocol is used. This paper studies online transmission policies for an energy harvesting transmitter. Unlike the existing online policies which more or less require the knowledge on the future behavior of the energy and data arrival processes, we consider a practical but significantly more challenging scenario where the energy and data arrival processes are assumed to be totally unknown. Our design is formulated as a robust-optimal control problem which aims to optimize the worst-case performance. The transmission policy is designed only based on the current battery energy level and the data queue length directly monitored by the transmitter itself. Specifically, we apply an event-trigger approach in which the transmitter continuously monitors the battery energy and data queue length, and triggers an event when a significant change occurs in either of them. Once an event is triggered, the transmission policy is updated by the solution to the robust-optimal control problem. We consider both the transmission time and throughput as the performance metrics and formulated two optimization problems. The solutions are given in either a simple analytical form or an easy-to-implement algorithm.