We consider a joint sensor and controller design problem for linear Gaussian stochastic systems in which a weighted sum of quadratic control cost and the amount of information acquired by the sensor is minimized. This problem formulation is motivated by situations where a control law must be designed in the presence of sensing, communication, and privacy constraints. We show that the optimal joint sensor-controller design is relatively easy when the sensing policy is restricted to be linear. Namely, an explicit form of the optimal linear sensor equation, the Kalman filter, and the certainty equivalence controller that jointly solves the problem can be efficiently found by semidefinite programming (SDP). Whether the linearity assumption in our design is restrictive or not is currently an open problem.
However, the majority of the existing work in this context assume sensor models and or channel models , and are different from ). A few exceptions include @cite_13 and @cite_26 , where sensor-controller joint design problems are considered. However, these works are concerned with sensor power constraints rather than information constraints, and are different from ). Our problem formulation ) falls into a general class of sensor optimization problems considered in @cite_17 , where several results are derived regarding the convexity of the problem and the existence of an optimal solution under different choices of topologies in the space of sensors. However, no structural results on specific problems appear there.
@cite_26 @cite_13 @cite_17
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We consider a Wireless Sensor Network where each sensor device is able to harvest energy from the environment, and randomly accesses the channel to transmit packets of random importance to a fusion center. If a collision occurs, the transmission fails and all packets involved are discarded. We design distributed transmission schemes where each sensor node, based on its own energy level and the importance of its own data packet, decides whether to transmit the packet or remain idle, so as to maximize the network utility, defined as the average long-term aggregate network importance of the data packets successfully reported to the fusion center. Due to the generally non-convex structure of the optimization problem, we resort to approximate solutions. In particular, we use a mathematical artifice based on a game theoretic formulation of the multiaccess problem, where each sensor node is a player that attempts to selfishly maximize the network utility. We characterize the Symmetric Nash Equilibrium (SNE) of this game, where all the sensor nodes employ the same policy. We prove the existence and uniqueness of the SNE, and we show that it is a local maximum of the original optimization problem. Moreover, we derive an algorithm to compute it. In this paper, we study the problem of tracking an object moving randomly through a network of wireless sensors. Our objective is to devise strategies for scheduling the sensors to optimize the tradeoff between tracking performance and energy consumption. We cast the scheduling problem as a partially observable Markov decision process (POMDP), where the control actions correspond to the set of sensors to activate at each time step. Using a bottom-up approach, we consider different sensing, motion and cost models with increasing levels of difficulty. At the first level, the sensing regions of the different sensors do not overlap and the target is only observed within the sensing range of an active sensor. Then, we consider sensors with overlapping sensing range such that the tracking error, and hence the actions of the different sensors, are tightly coupled. Finally, we consider scenarios wherein the target locations and sensors' observations assume values on continuous spaces. Exact solutions are generally intractable even for the simplest models due to the dimensionality of the information and action spaces. Hence, we devise approximate solution techniques, and in some cases derive lower bounds on the optimal tradeoff curves. The generated scheduling policies, albeit suboptimal, often provide close-to-optimal energy-tracking tradeoffs. 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. 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. Wireless Heterogeneous Sensor Network (WHSN) facilitates ubiquitous information acquisition for Ambient Intelligence (AmI) systems. It is of great importance of power management and topology control for WHSN to achieve desirable network performances, such as clustering properties, connectivity and power efficiency. This paper proposes a game theoretic model of topology control to analyze the decentralized interactions among heterogeneous sensors. We study the utility function for nodes to achieve desirable frame success rate and node degree, while minimizing the power consumption. Specifically, we propose a static complete-information game formulation for power scheduling and then prove the existence of the Nash equilibrium with simultaneous move. Because the heterogeneous sensors typically react to neighboring environment based on local information and the states of sensors are evolving over time, the power-scheduling problem in WHSN is further formulated into a more realistic incomplete-information dynamic game model with sequential move. We then analyze the separating equilibrium, one of the perfect Bayesian equilibriums resulted from the dynamic game, with the sensors revealing their operational states from their actions. The sufficient and necessary conditions for the existence of separating equilibrium are derived for the dynamic Bayesian game, which provide theoretical basis to the proposed power scheduling algorithms, NEPow and BEPow. The primary contributions of this paper include applying game theory to analyze the distributed decision-making process of individual sensor nodes and to analyze the desirable utilities of heterogeneous sensor nodes. Simulations are presented to validate the proposed algorithms and the results show their ability of maintaining reliable connectivity, reducing power consumption, while achieving desirable network performances. This study considers an integrated topology control and routing problem in wireless sensor networks (WSNs), which are employed to gather data via use of sensors with limited energy resources. We employ a hierarchical topology and routing structure with multiple sinks and devise a topology control scheme via usable energy fraction at the sensors. We develop and examine three different mathematical models whose solutions prescribe clusterhead and sink locations and data routing from sensors to sinks in a period of a deployment cycle. We develop a heuristic solution algorithm which provides very small optimality gaps for the models. The approach utilizes two types of solution representations, a combination of multiple neighborhoods, and objective value-based cut inequalities for improving the evaluation of candidate solutions. We present extensive numerical test results and analysis of the models and the solution approach. We determine that our proposed model, which minimizes average energy usage and the range of remaining energy distribution at the sensors, captures important characteristics of topology control and routing integration in WSN design and exhibits significantly better performance than our benchmark models and a well-known protocol HEED in extending network lifetime. In a large and complex distributed sensor network, the individual sensor directly communicates only with its neighboring sensors. Despite being restricted to such local communications, the network itself should be self-organizing to maintain certain desirable properties, such as network connectivity and lifetime maximization. Topology control is a technique to determine the optimal transmit parameters for each sensor, such that the network topology has the best possible network performance. In this paper, we investigate a dynamic topology control scheme to improve the network lifetime for wireless sensor networks in the presence of selfish sensors. A non-cooperative game aided topology control approach is developed for designing energy-efficient and energy balanced network topologies dynamically. Each sensor in the topology control game tries to minimize its unwillingness for constructing a connected network according to its residual energy and transmit power. We prove the existence of Nash equilibrium (NE) and demonstrate that the NE is Pareto optimal as well. Specifically, a fully distributed algorithm-topology control with lifetime extension (TCLE)-is proposed to construct dynamic network topologies. The topologies derived by TCLE algorithm can improve the network lifetime significantly as compared with existing algorithms. Simulations demonstrate the efficiency of our TCLE algorithm. Consider a set of sensors estimating the state of a process in which only one of these sensors can operate at each time-step due to constraints on the overall system. The problem addressed here is to choose which sensor should operate at each time-step to minimize a weighted function of the error covariance of the state estimation at each time-step. This work investigates the development of tractable algorithms to solve for the optimal and suboptimal sensor schedule. First, a condition on the non-optimality of an initialization of the schedule is presented. Second, using this condition, both an optimal and a suboptimal algorithm are devised to prune the search tree of all possible sensor schedules. This pruning enables the solution of larger systems and longer time horizons than with enumeration alone. The suboptimal algorithm trades off the quality of the solution and the complexity of the problem through a tuning parameter. Third, a hierarchical algorithm is formulated to decrease the computation time of the suboptimal algorithm by using results from a low complexity solution to further prune the tree. Numerical simulations are performed to demonstrate the performance of the proposed algorithms. Linear-Quadratic-Gaussian (LQG) control is concerned with the design of an optimal controller and estimator for linear Gaussian systems with imperfect state information. Standard LQG assumes the set of sensor measurements, to be fed to the estimator, to be given. However, in many problems, arising in networked systems and robotics, one may not be able to use all the available sensors, due to power or payload constraints, or may be interested in using the smallest subset of sensors that guarantees the attainment of a desired control goal. In this paper, we introduce the sensing-constrained LQG control problem, in which one has to jointly design sensing, estimation, and control, under given constraints on the resources spent for sensing. We focus on the realistic case in which the sensing strategy has to be selected among a finite set of possible sensing modalities. While the computation of the optimal sensing strategy is intractable, we present the first scalable algorithm that computes a near-optimal sensing strategy with provable sub-optimality guarantees. To this end, we show that a separation principle holds, which allows the design of sensing, estimation, and control policies in isolation. We conclude the paper by discussing two applications of sensing-constrained LQG control, namely, sensing-constrained formation control and resource-constrained robot navigation. This paper addresses the coverage breach problem in wireless sensor networks with limited bandwidths. In wireless sensor networks, sensor nodes are powered by batteries. To make efficient use of battery energy is critical to sensor network lifetimes. When targets are redundantly covered by multiple sensors, especially in stochastically deployed sensor networks, it is possible to save battery energy by organizing sensors into mutually exclusive subsets and alternatively activating only one subset at any time. Active nodes are responsible for sensing, computing and communicating. While the coverage of each subset is an important metric for sensor organization, the size of each subset also plays an important role in sensor network performance because when active sensors periodically send data to base stations, contention for channel access must be considered. The number of available channels imposes a limit on the cardinality of each subset. Coverage breach happens when a subset of sensors cannot completely cover all the targets. To make efficient use of both energy and bandwidth with a minimum coverage breach is the goal of sensor network design. This paper presents the minimum breach problem using a mathematical model, studies the computational complexity of the problem, and provides two approximate heuristics. Effects of increasing the number of channels and increasing the number of sensors on sensor network coverage are studied through numerical simulations. Overall, the simulation results reveal that when the number of sensors increases, network lifetimes can be improved without loss of network coverage if there is no bandwidth constraint; with bandwidth constraints, network lifetimes may be improved further at the cost of coverage breach. Retentive (memory-utilizing) sensing-acting agents may operate under limitations on the communication between their sensing, memory and acting components, requiring them to trade off the external cost that they incur with the capacity of their communication channels. In this paper we formulate this problem as a sequential rate-distortion problem of minimizing the rate of information required for the controller's operation under a constraint on its external cost. We reduce this bounded retentive control problem to the memoryless one, studied in Part I of this work, by viewing the memory reader as one more sensor and the memory writer as one more actuator. We further investigate the structure of the resulting optimal solution and demonstrate its interesting phenomenology. This paper studies a remote state estimation problem where a sensor, equipped with energy harvesting capabilities, observes a dynamical process and transmits local state estimates over a packet dropping channel to a remote estimator. The objective is to decide, at every discrete time instant, whether the sensor should transmit or not, in order to minimize the expected estimation error covariance at the remote estimator over a finite horizon, subject to constraints on the sensor’s battery energy governed by an energy harvesting process. We establish structural results on the optimal scheduling which show that, for a given battery energy level and a given harvested energy, the optimal policy is a threshold policy on the error covariance. Similarly, for a given error covariance and a given harvested energy, the optimal policy is a threshold policy on the current battery level. An extension to the problem of transmission scheduling and control with an energy harvesting sensor is also considered. We take a top-down approach of formulating the rate control problem, over a collection tree, in a wireless sensor network as a generic convex optimization problem and propose a distributed back pressure algorithm using Lyapunov drift based optimization techniques. Primarily, we show that existing theoretical results in the field of stochastic network optimization can be directly applied to a CSMA based wireless sensor network using our novel receiver capacity model. We back this claim by implementing our algorithm on the Tmote sky class devices. Our experimental evaluation on a 5 node testbed shows that the empirically observed rate allocation on a real sensor network testbed that uses our back pressure algorithm is close to the analytically predicted values, justifying our claims. We consider the problem of decentralized detection under constraints on the number of bits that can be transmitted by each sensor. In contrast to most previous work, in which the joint distribution of sensor observations is assumed to be known, we address the problem when only a set of empirical samples is available. We propose a novel algorithm using the framework of empirical risk minimization and marginalized kernels, and analyze its computational and statistical properties both theoretically and empirically. We provide an efficient implementation of the algorithm, and demonstrate its performance on both simulated and real data sets. Established approaches to data aggregation in wireless sensor networks (WSNs) do not cover the variety of new use cases developing with the advent of the Internet of Things (IoT). In particular, the current push toward fog computing, in which control, computation, and storage are moved to nodes close to the network edge, induces a need to collect data at multiple sinks, rather than the single sink typically considered in WSN aggregation algorithms. Moreover, for machine-to-machine communication scenarios, actuators subscribing to sensor measurements may also be present, in which case data should be not only aggregated and processed in-network but also disseminated to actuator nodes. In this paper, we present mixed-integer programming formulations and algorithms for the problem of energy-optimal routing and multiple-sink aggregation, as well as joint aggregation and dissemination, of sensor measurement data in IoT edge networks. We consider optimization of the network for both minimal total energy usage, and min-max per-node energy usage. We also provide a formulation and algorithm for throughput-optimal scheduling of transmissions under the physical interference model in the pure aggregation case. We have conducted a numerical study to compare the energy required for the two use cases, as well as the time to solve them, in generated network scenarios with varying topologies and between 10 and 40 nodes. Although aggregation only accounts for less than 15 of total energy usage in all cases tested, it provides substantial energy savings. Our results show more than 13 times greater energy usage for 40-node networks using direct, shortest-path flows from sensors to actuators, compared with our aggregation and dissemination solutions. In this paper, we address the problem of optimizing the detection performance of sensor networks under communication constraints on the common access channel. Our work helps understanding tradeoffs between sensor network para-meters like number of sensors, degree of quantization at each local sensor, and SNR. Traditionally, this problem is tack-led using asymptotic assumptions on the number of sensors, an approach that leads to the abstraction of important details such as the structure of the fusion center. We adopt a non-asymptotic approach and optimize both, the sensing and the fusion sides with respect to the probability of detection error. We show that the optimal fusion rule has an interesting structure similar to themajority-voting rule. In addition, we study the convergence with respect to the number of sensors of the performance of the fusion rule. We show that convergence is SNR dependent and that, in low-SNR environments, asymptotics may require a large number of sensors. Random key predistribution scheme of Eschenauer and Gligor (EG) is a typical solution for ensuring secure communications in a wireless sensor network (WSN). Connectivity of the WSNs under this scheme has received much interest over the last decade, and most of the existing work is based on the assumption of unconstrained sensor-to-sensor communications. In this paper, we study the k-connectivity of WSNs under the EG scheme with physical link constraints; k-connectivity is defined as the property that the network remains connected despite the failure of any (k - 1) sensors. We use a simple communication model, where unreliable wireless links are modeled as independent on off channels, and derive zero-one laws for the properties that i) the WSN is k-connected, and ii) each sensor is connected to at least k other sensors. These zero-one laws improve the previous results by Rybarczyk on the k-connectivity under a fully connected communication model. Moreover, under the on off channel model, we provide a stronger form of the zero-one law for the 1-connectivity as compared to that given by Yagan. We consider a wireless sensor network consisting of n sensors, each having a recorded bit, the sensor’s measurement, which has been set to either “0” or “1”. The network has a special node called the fusion center whose goal is to compute a symmetric function of these bits; i.e., a function that depends only on the number of sensors that have a “1.” The sensors convey information to the fusion center in a multi-hop fashion to enable the function computation. The problem studied is to minimize the total transmission energy used by the network when computing this function, subject to the constraint that this computation is correct with high probability. We assume the wireless channels are binary symmetric channels with a probability of error p, and that each sensor uses rαunits of energy to transmit each bit, where r is the transmission range of the sensor. The main result in this paper is an algorithm whose energy usage is Θ (n(loglogn)(√logn n)α), and we also show that any algorithm satisfying the performance constraints must necessarily have energy usage Ω (n(√logn n)α). Then, we consider the case where the sensor network observes N events, and each node records one bit per event, thus having N bits to convey. The fusion center now wants to compute N symmetric functions, one for each of the events. The problem of binary hypothesis testing is considered in a bandwidth-constrained densely populated low-power wireless sensor network operating over insecure links. Observations of the sensors are quantized and encrypted before transmission. The encryption method maps the output of the quantizer to one of the possible quantizer output levels randomly according to a probability matrix. The intended (ally) fusion center (AFC) is aware of the encryption keys (probabilities) while the unauthorized (third party) fusion center (TPFC) is not. A constrained optimization problem is formulated from the point of view of AFC in order to design its decision rule along with the encryption probabilities. The objective function to be minimized is the error probability of AFC and the constraint is a lower bound on the error probability of TPFC. In the binary case the optimal solution is found and in the nonbinary case a good suboptimal solution is analytically obtained. Numerical results are presented to show that it is possible to degrade the error probability of TPFC significantly and still achieve very low probability of error for AFC. The proposed method which may be considered a PHY-layer security scheme is highly scalable since it does not increase the packet overhead or transmit power of the sensors and has very low computational complexity. A scheme is described to randomize the keys so as to defeat any key space exploration attack. In this paper basic results on distributed detection are reviewed. In particular we consider the parallel and the serial architectures in some detail and discuss the decision rules obtained from their optimization based an the Neyman-Pearson (NP) criterion and the Bayes formulation. For conditionally independent sensor observations, the optimality of the likelihood ratio test (LRT) at the sensors is established. General comments on several important issues are made including the computational complexity of obtaining the optimal solutions the design of detection networks with more general topologies, and applications to different areas.