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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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). 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. Motivated by limited computational resources in sensor nodes, the impact of complexity constraints on the communication efficiency of sensor networks is studied. A single-parameter characterization of processing limitation of nodes in sensor networks is invoked. Specifically, the relaying nodes are assumed to "donate" only a small part of their total processor time to relay other nodes information. The amount of donated processor time is modelled by the node's ability to decode a channel code reliably at given rate R. Focusing on a four node network, with two relays, prior work for a complexity constrained single relay network is built upon. In the proposed coding scheme, the transmitter sends a broadcast code such that the relays decode only the "coarse" information, and assist the receiver in removing ambiguity only in that information. Via numerical examples, the impact of different power constraints in the system, ranging from per node power bound to network wide power constraint is explored. As the complexity bound R increases, the proposed scheme becomes identical to the recently proposed achievable rate by Gupta & Kumar (2003). Both discrete memoryless and Gaussian channels are considered. Accurate analytical expressions of delay and packet reception probabilities, and energy consumption of duty-cycled wireless sensor networks with random medium access control (MAC) are instrumental for the efficient design and optimization of these resource-constrained networks. Given a clustered network topology with unslotted IEEE 802.15.4 and preamble sampling MAC, a novel approach to the modeling of the delay, reliability, and energy consumption is proposed. The challenging part in such a modeling is the random MAC and sleep policy of the receivers, which prevents to establish the exact time of data packet transmission. The analysis gives expressions as function of sleep time, listening time, traffic rate and MAC parameters. The analytical results are then used to optimize the duty cycle of the nodes and MAC protocol parameters. The approach provides a significant reduction of the energy consumption compared to existing solutions in the literature. Monte Carlo simulations by ns2 assess the validity of the analysis. In a sensor network, in practice, the communication among sensors is subject to: 1) errors that can cause failures of links among sensors at random times; 2) costs; and 3) constraints, such as power, data rate, or communication, since sensors and networks operate under scarce resources. The paper studies the problem of designing the topology, i.e., assigning the probabilities of reliable communication among sensors (or of link failures) to maximize the rate of convergence of average consensus, when the link communication costs are taken into account, and there is an overall communication budget constraint. We model the network as a Bernoulli random topology and establish necessary and sufficient conditions for mean square sense (mss) and almost sure (a.s.) convergence of average consensus when network links fail. In particular, a necessary and sufficient condition is for the algebraic connectivity of the mean graph topology to be strictly positive. With these results, we show that the topology design with random link failures, link communication costs, and a communication cost constraint is a constrained convex optimization problem that can be efficiently solved for large networks by semidefinite programming techniques. Simulations demonstrate that the optimal design improves significantly the convergence speed of the consensus algorithm and can achieve the performance of a non-random network at a fraction of the communication cost. Consider a control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We study the fundamental tradeoff between the communication rate @math bits sec and the expected cost @math . We obtain a lower bound on a certain rate-cost function, which quantifies the minimum directed mutual information between the channel input and output that is compatible with a target LQR cost. The rate-cost function has operational significance in multiple scenarios of interest: among others, it allows us to lower-bound the minimum communication rate for fixed and variable length quantization, and for control over noisy channels. We derive an explicit lower bound to the rate-cost function, which applies to the vector, non-Gaussian, and partially observed systems, thereby extending and generalizing an earlier explicit expression for the scalar Gaussian system, due to Tatikonda el al. The bound applies as long as the system noise has a probability density function. It can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state. Via a separation principle between control and communication, similar results hold for causal lossy compression of additive noise Markov sources. Apart from standard dynamic programming arguments, our technical approach leverages the Shannon lower bound, develops new estimates for data compression with coding memory, and uses some recent results on high resolution variable-length vector quantization to prove that the new converse bounds are tight. 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. Despite much research on probabilistic key predistribution schemes for wireless sensor networks over the past decade, few formal analyses exist that define schemes’ resilience to node-capture attacks precisely and under realistic conditions. In this paper, we analyze the resilience of the @math -composite key predistribution scheme, which mitigates the node capture vulnerability of the Eschenauer-Gligor scheme in the neighbor discovery phase. We derive scheme parameters to have a desired level of resiliency, and obtain optimal parameters that defend against different adversaries as much as possible. We also show that this scheme can be easily enhanced to achieve the same “perfect resilience” property as in the random pairwise key predistribution for attacks launched after neighbor discovery. Despite considerable attention to this scheme, much prior work explicitly or implicitly uses an incorrect computation for the probability of link compromise under node-capture attacks and ignores the real-world transmission constraints of sensor nodes. Moreover, we derive the critical network parameters to ensure connectivity in both the absence and presence of node-capture attacks. We also investigate node replication attacks by analyzing the adversary’s optimal strategy. Due to their low cost and small form factors, a large number of sensor nodes can be deployed in redundant fashion in dense sensor networks. The availability of redundant nodes increases network lifetime as well as network fault tolerance. It is, however, undesirable to keep all the sensor nodes active at all times for sensing and communication. An excessive number of active nodes lead to higher energy consumption and it places more demand on the limited network bandwidth. We present an efficient technique for the selection of active sensor nodes in dense sensor networks. The active node selection procedure is aimed at providing the highest possible coverage of the sensor field, i.e., the surveillance area. It also assures network connectivity for routing and information dissemination. We first show that the coverage-centric active nodes selection problem is NP-complete. We then present a distributed approach based on the concept of a connected dominating set (CDS). We prove that the set of active nodes selected by our approach provides full coverage and connectivity. We also describe an optimal coverage-centric centralized approach based on integer linear programming. We present simulation results obtained using an ns2 implementation of the proposed technique. 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. We investigate the secure connectivity of wireless sensor networks under the random key distribution scheme of Eschenauer and Gligor. Unlike recent work which was carried out under the assumption of full visibility, here we assume a (simplified) communication model where unreliable wireless links are represented as on off channels. We present conditions on how to scale the model parameters so that the network: 1) has no secure node which is isolated and 2) is securely connected, both with high probability when the number of sensor nodes becomes large. The results are given in the form of full zero-one laws, and constitute the first complete analysis of the EG scheme under non-full visibility. Through simulations, these zero-one laws are shown to be valid also under a more realistic communication model (i.e., the disk model). The relations to the Gupta and Kumar's conjecture on the connectivity of geometric random graphs with randomly deleted edges are also discussed. A point-to-point wireless communication system in which the transmitter is equipped with an energy harvesting device and a rechargeable battery, is studied. Both the energy and the data arrivals at the transmitter are modeled as Markov processes. Delay-limited communication is considered assuming that the underlying channel is block fading with memory, and the instantaneous channel state information is available at both the transmitter and the receiver. The expected total transmitted data during the transmitter's activation time is maximized under three different sets of assumptions regarding the information available at the transmitter about the underlying stochastic processes. A learning theoretic approach is introduced, which does not assume any a priori information on the Markov processes governing the communication system. In addition, online and offline optimization problems are studied for the same setting. Full statistical knowledge and causal information on the realizations of the underlying stochastic processes are assumed in the online optimization problem, while the offline optimization problem assumes non-causal knowledge of the realizations in advance. Comparing the optimal solutions in all three frameworks, the performance loss due to the lack of the transmitter's information regarding the behaviors of the underlying Markov processes is quantified. We consider the problem of resource allocation in downlink OFDMA systems for multi service and unknown environment. Due to users' mobility and intercell interference, the base station cannot predict neither the Signal to Noise Ratio (SNR) of each user in future time slots nor their probability distribution functions. In addition, the traffic is bursty in general with unknown arrival. The probability distribution functions of the SNR, channel state and traffic arrival density are then unknown. Achieving a multi service Quality of Service (QoS) while optimizing the performance of the system (e.g. total throughput) is a hard and interesting task since it depends on the unknown future traffic and SNR values. In this paper we solve this problem by modeling the multiuser queuing system as a discrete time linear dynamic system. We develop a robust H∞ controller to regulate the queues of different users. The queues and Packet Drop Rates (PDR) are controlled by proposing a minimum data rate according to the demanded service type of each user. The data rate vector proposed by the controller is then fed as a constraint to an instantaneous resource allocation framework. This instantaneous problem is formulated as a convex optimization problem for instantaneous subcarrier and power allocation decisions. Simulation results show small delays and better fairness among users. This paper characterizes the performance in terms of queueing stability of a network composed of multiple MIMO transmitter-receiver pairs taking into account the dynamic traffic pattern and the probing feedback cost. We adopt a centralized scheduling scheme that selects a number of active pairs in each time-slot. We consider that the transmitters apply interference alignment (IA) technique if two or more pairs are active, whereas in the special case where one pair is active point-to-point MIMO singular value decomposition (SVD) is used. We consider a time-division duplex (TDD) system where transmitters acquire their channel state information (CSI) by decoding the pilot sequences sent by the receivers. Since global CSI knowledge is required for IA, the transmitters have also to exchange their estimated CSIs over a backhaul of limited capacity (i.e. imperfect case). Under this setting, we characterize in this paper the stability region of the system under both the imperfect and perfect (i.e. unlimited backhaul) cases, then we examine the gap between these two resulting regions. Further, under each case we provide a centralized probing policy that achieves the max stability region. These stability regions and scheduling policies are given for the symmetric system, where all the path loss coefficients are equal to each other, as well as for the general system. For the symmetric system, we provide the conditions under which IA yields a queueing stability gain compared to SVD. Under the general system, the adopted scheduling policy is of a high computational complexity for moderate numbers of pairs, consequently we propose an approximate policy that has a reduced complexity but that achieves only a fraction of the system stability region. A characterization of this fraction is provided. We investigate the resiliency of IEEE802.11 rate adaptation algorithms (RAA) against smart jamming attacks. We consider several classes of state-of-the-art RAAs that include the SampleRate, ONOE, AMRR, and the RAA used in Atheros Microsoft Windows XP driver. We model the behavior of these algorithms, and show the existence of very efficient attacks that exploit RAA-specific vulnerabilities as well as the inherent weaknesses that exist in the design of IEEE802.11 MAC and link layer protocol: in particular the overt packet rate information being transmitted, predictable rate selection mechanism, performance anomaly caused by the equiprobability of transmissions among all nodes regardless of the data rates being employed, and the lack of interference differentiation from poor link quality by IEEE802.11 RAAs. In this work, we present algorithms that determine optimal jamming strategies against RAAs for a given jamming budget, and experimentally demonstrate the efficiency of these smart jamming attacks, which can be orders of magnitude more efficient than naive jamming. For example, in the case of SampleRate, eight reactive jamming pulses every second are sufficient to achieve the same network throughput degradation achieved by a periodic jammer with the jamming energy cost 100 times higher. Some of the RAAs react even worse to smart jamming attacks; ONOE in particular suffers from the phenomenon of congestion collapse where the nodes fail to recover from the lowest data rate even after the jammer stops jamming. At the end, we summarize fundamental reasons behind such RAA vulnerabilities and propose a preliminary set of mitigation techniques. We leave the experimental demonstration of the efficiency of the proposed mitigation mechanisms for future work. We consider the network reliability problem in secure wireless sensor networks that employ a heterogeneous random key predistribution scheme. This scheme is introduced recently, as a generalization of the Eschenauer-Gligor scheme, to account for the cases when the network comprises sensors with varying level of resources or connectivity requirements; e.g., regular nodes vs. cluster heads. The scheme induces the inhomogeneous random key graph, denoted G(n;μ,K, P ), where each of the n nodes are independently assigned to one of r classes according to a probability distribution μ = (μ1, . . . , μr) and then a class-i node is assigned Ki keys uniformly at random from a pool of size P ; two nodes that share a key are then connected by an edge. We analyze the reliability of G(n;μ,K, P ) against random link failures. Namely, we consider G(n;μ,K, P, α) formed by deleting each edge of G(n;μ,K, P ) independently with probability 1 − α, and study the probability that the resulting graph i) has no isolated node; and ii) is connected. We present scaling conditions on K , P , and α such that both events take place with probability zero or one, respectively, as the number of nodes gets large. We also present numerical results to support these zero-one laws in the finite-node regime. A novel control strategy for multi-agent coordination with event-based broadcasting is presented. In particular, each agent decides itself when to transmit its current state to its neighbors and the local control laws are based on these sampled state measurements. Three scenarios are analyzed: Networks of single-integrator agents with and without communication delays, and networks of double-integrator agents. The novel event-based scheduling strategy bounds each agent's measurement error by a time-dependent threshold. For each scenario it is shown that the proposed control strategy guarantees either asymptotic convergence to average consensus or convergence to a ball centered at the average consensus. Moreover, it is shown that the inter-event intervals are lower-bounded by a positive constant. Numerical simulations show the effectiveness of the novel event-based control strategy and how it compares to time-scheduled control. We present a general intrinsic tracking controller design for fully-actuated simple mechanical systems, when the configuration space is one of a general class of Lie groups. We first express a state-feedback controller in terms of a function-the "error function"-satisfying certain regularity conditions. If an error function can be found, then a general smooth and bounded reference trajectory may be tracked asymptotically from almost every initial condition, with locally exponential convergence. Asymptotic convergence from almost every initial condition is referred to as "almost-global" asymptotic stability. Error functions may be shown to exist on any compact Lie group, or any Lie group diffeomorphic to the product of a compact Lie group and R sup n . This covers many cases of practical interest, such as SO(n), SE(n), their subgroups, and direct products. We show here that for compact Lie groups the dynamic configuration-feedback controller obtained by composing the full state-feedback law with an exponentially convergent velocity observer is also almost-globally asymptotically stable with respect to the tracking error. We emphasize that no invariance is needed for these results. However, for the special case where the kinetic energy is left-invariant, we show that the explicit expression of these controllers does not require coordinates on the Lie group. The controller constructions are demonstrated on SO(3), and simulated for the axi-symmetric top. Results show excellent performance. The problem of distributed detection and estimation in a sensor network over a multiaccess fading channel is considered. A communication scheme known as the type-based random access (TBRA) is employed and its performance is characterized with respect to the mean transmission rate and the channel coherence index. For extreme values of channel coherence index i.e., 0 and infin, we give an optimal TBRA scheme which is essentially a sensor activation strategy that achieves the optimal allocation of transmission energy to spatial and temporal domains. For channels with zero coherence index, it is shown that there exists a finite optimal mean transmission rate maximizing performance. This optimal rate can be calculated numerically or estimated using the Gaussian approximation. On the other hand, for channels with infinite coherence index (i.e., no fading) the optimal strategy is to allocate all the energy to the spatial domain. Numerical examples and simulations confirm our theory. This paper investigates the noncoherent detection in a two-way relay channel operated with physical-layer network coding (PNC), assuming FSK modulation and short-packet transmissions. For noncoherent detection, the detector has access to the magnitude but not the phase of the received signal. For conventional communication in which a receiver receives the signal from a transmitter only, the phase does not affect the magnitude, and hence the performance of the noncoherent detector is independent of the phase. PNC, on the other hand, is a multiuser system in which a receiver receives signals from multiple transmitters simultaneously. The relative phase of the signals from different transmitters affects the received signal magnitude through constructive-destructive interference. In particular, for good performance, the noncoherent detector of a multiuser system such as PNC must take into account the influence of the relative phase on the signal magnitude. Building on this observation, this paper delves into the fundamentals of PNC noncoherent detector design. To avoid excessive overhead, we assume a set-up in which the short packets in the PNC system do not have preambles. We show how the relative phase can be deduced directly from the magnitudes of the received data symbols, and that the knowledge of the relative phase thus deduced can in turn be used to enhance performance of noncoherent detection. Our overall detector design consists of two components: 1) a channel gains estimator that estimates channel gains without preambles; and 2) a detector that builds on top of the estimated channel gains to jointly estimate relative phase and detect data using a belief propagation algorithm. Numerical results show that our detector performs nearly as well as a “fictitious” optimal detector that has perfect knowledge of the channel gains and relative phase. Although this paper focuses on PNC with FSK modulation, we believe that the insight of this paper applies generally to noncoherent detection in other multiuser systems with other modulations. Specifically, our insight is that the relative phase of overlapped signals affects the signal magnitude in multiuser systems, but fortunately the relative phase can be deduced from the magnitudes and this knowledge can be used to improve the detection performance.