Distributed privacy-preserving network size computation: A system-identification based method

In this study, we propose an algorithm for computing the network size of communicating agents. The algorithm is distributed: a) it does not require a leader selection; b) it only requires local exchange of information, and; c) its design can be implemented using local information only, without any global information about the network. It is privacy-preserving, namely it does not require to propagate identifying labels. This algorithm is based on system identification, and more precisely on the identification of the order of a suitably-constructed discrete-time linear time-invariant system over some finite field. We provide a probabilistic guarantee for any randomly picked node to correctly compute the number of nodes in the network. Moreover, numerical implementation has been taken into account to make the algorithm applicable to networks of hundreds of nodes, and therefore make the algorithm applicable in real-world sensor or robotic networks. We finally illustrate our results in simulation and conclude the paper with discussions on how our technique differs from a previously-known strategy based on statistical inference.Comment: 52nd IEEE Conference on Decision and Control (CDC 2013) (2013

Optimal one-dimensional coverage by unreliable sensors

This paper regards the problem of optimally placing unreliable sensors in a one-dimensional environment. We assume that sensors can fail with a certain probability and we minimize the expected maximum distance from any point in the environment to the closest active sensor. We provide a computational method to find the optimal placement and we estimate the relative quality of equispaced and random placements. We prove that the former is asymptotically equivalent to the optimal placement when the number of sensors goes to infinity, with a cost ratio converging to 1, while the cost of the latter remains strictly larger.Comment: 21 pages 2 figure

Input and State Observability of Network Systems with a Single Unknown Input

International audienceThis paper studies network systems affected by a single unknown input, possibly representing an attack or a failure, to be estimated. The main result is a characterization of input and state observability, namely the conditions under which both the whole network state and the unknown input can be reconstructed from some measured local states. This characterization is in terms of observability of a suitably-defined subsystem, which allows the use of known graphical charactizations of observability of network systems, leading to structural results (true for almost all interaction weights) or strong structural results (true for all non-zero interaction weights). We apply our results to an illustrative example, finding a full characterization of input and state observability of a path graph, affected by a single unknown input and with measurement of a small number of local states

Generic Delay-L Left Invertibility of Structured Systems

International audienceThis paper studies structured systems, namely linear systems where the state-space matrices have zeros in some fixed positions and free parameters in all other entries. This paper focuses on time-invariant systems in discrete time affected by an unknown input, and their delay-L left invertibility, namely the possibility to reconstruct the input sequence from the output sequence, assuming that the initial state is known, and requiring that the inputs can be reconstructed up to L time steps before the current output. Building upon classical results on linear systems theory and on structured systems, a graphical characterization is obtained of the integers L for which a structured system is generically delay-L left invertible

Unbiased Filtering for State and Unknown Input with Delay

International audienceIn this paper, we consider linear network systems with unknown inputs. We present an unbiased recursive algorithm that simultaneously estimates states and inputs. We focus on delay-left invertible systems with intrinsic delay l ≥ 1, where the input reconstruction is possible only by using outputs up to l time steps later in the future. By showing an equivalence with a descriptor system, we state conditions under which the time-varying filter converges to a stationary stable filter, involving the solution of a discrete-time algebraic Riccati equation

Source Localization by Gradient Estimation Based on Poisson Integral

International audienceWe consider the problem of localizing the source of a diffusion process. The source is supposed to be isotropic, and several sensors, equipped on a vehicle moving without position information, provide pointwise measures of the quantity being emitted. The solution we propose is based on computing the gradient -- and higher-order derivatives such as the Hessian -- from Poisson integrals: in opposition to other solutions previously proposed, this computation does neither require specific knowledge of the solution of the diffusion process, nor the use of probing signals, but only exploits properties of the PDE describing the diffusion process. The theoretical results are illustrated by simulations

Distributed Source Seeking without Global Position Information

International audienceWe present a distributed control law to steer a group of autonomous communicating sensors towards the source of a diffusion process. The graph describing the communication links between sensors has a time-invariant topology, and each sensor is able to measure (in addition to the quantity of interest) only the relative bearing angle with respect to its neighbour, but has no absolute position information and does not know any relative distance. Using multiple sensors is useful in wide environments (e.g., under the sea), or when the function describing the diffusion process is slowly changing in space, so that a single sensor may have to travel long distances before having a good gradient estimation. Our approach is based on a twofold control law, which is able to bring and keep the set of sensors on a circular equispaced formation, and to steer the circular formation towards the source via a gradient-ascent technique. The effectiveness of the proposed algorithm is both theoretically proven and supported by simulation results

Towards scalable optimal traffic control

International audienceThis paper deals with scalable control of traffic lights in urban traffic networks. Optimization is done in real time, so as to take into account variable traffic demands.At each cycle of the traffic lights, the optimization concerns times instants where each traffic light starts and ends its green phase: this allows to describe both the duty-cycle and the phase shifts.First, we formulate a global optimization problem, which can be cast as a mixed-integer linear program. To overcome the complexity of this centralized approach, we also propose a decentralized suboptimal algorithm, whose simplicity allows on-line implementation. Simulations show the effectiveness of the proposed strategies

Distributed averaging on digital erasure networks

International audience; Iterative distributed algorithms are studied for computing arithmetic averages over networks of agents connected through memoryless broadcast erasure channels. These algorithms do not require the agents to have any knowledge about the global network structure or size. Almost sure convergence to state agreement is proved, and the communication and computational complexities of the algorithms are analyzed. Both the number of transmissions and the number of computations performed by each agent of the network are shown to grow not faster than poly-logarithmically in the desired precision. The impact of the graph topology on the algorithms' performance is analyzed as well. Moreover, it is shown how, in the presence of noiseless communication feedback, one can modify the algorithms, significantly improving their performance versus complexity trade-off

Generic Delay-L Left Invertibility of Structured Systems with Scalar Unknown Input

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