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In this paper a novel distributed algorithm for blind macro-calibration in sensor networks based on consensus is proposed. The algorithm is formulated as a set of gradient-type recursions for estimating parameters of sensor calibration functions, starting from local criteria defined as weighted sums of mean square differences between the outputs of neighboring sensors. It is proved that the algorithm achieves asymptotic agreement for sensor gains and offsets in the mean square sense and with probability one. In the case of additive measurement noise, additive inter-agent communication noise and communication outages, a modification of the original algorithm is proposed. It is proved using stochastic approximation arguments that the modified algorithm achieves asymptotic consensus for sensor gains and offsets in the mean square sense and with probability one. Special attention is paid to the situation when one sensor is selected as a reference. Illustrative simulation examples are provided.

In this paper, we propose a stochastic approximation algorithm for optimization of functions based on an adaptive extremum seeking method. The essence of this method is to approximate the gradient direction by introduction of a probing sequence, that is added to approximations and subsequently demodulated using an adaptive gain. Assuming that the probing and the demodulation signals are martingale difference sequences with adaptive diminishing gains, it is proved that the approximations converge almost surely to the optimizing value, under mild constraints on the measurement disturbance, and without assuming a priori boundedness of the approximation sequence. The measurement disturbance can contain a stochastic component, as well as a mean-square bounded deterministic component. The stochastic component can be nonstationary colored noise or a state-dependent random sequence. [ABSTRACT FROM AUTHOR]

In this paper a new distributed multi-agent Actor-Critic algorithm for reinforcement learning is proposed for solving multi-agent multi-task optimization problems. The Critic algorithm is in the form of a Distributed Emphatic Temporal Difference DETD(λ) algorithm, while the Actor algorithm is proposed as a complementary consensus based policy gradient algorithm, derived from a global objective function having the role of a scalarizing function in multi-objective optimization. It is demonstrated that the Feller-Markov properties hold for the newly derived Actor algorithm. A proof of the weak convergence of the algorithm to the limit set of an attached ODE is derived under mild conditions, using a specific decomposition between the Critic and the Actor algorithms and additional two-time-scale stochastic approximation arguments. An experimental verification of the algorithm properties is given, showing that the algorithm can represent an efficient tool for practice. [ABSTRACT FROM AUTHOR]

In this paper an approach is proposed to decentralized multi-agent identification of large-scale systems represented by linear discrete-time stochastic MIMO models. It is assumed that each agent: (a) has access only to a subset of noisy input–output variables; (b) communicates local data processing results to its neighborhood. The proposed algorithm consists of two stages. The first stage is a consensus-based stochastic approximation algorithm for estimating input–output correlation functions, while at the second stage each agent utilizes a stochastic approximation algorithm with expanding truncations derived from the modified Yule–Walker equations in order to generate all the system parameter estimates. It is proved that under nonrestrictive assumptions concerning the system properties and the multi-agent network topology the estimates of the correlation functions converge almost surely to their true values and those of the system parameters to a solution of the modified Yule–Walker equations, assuming intermittent observations and communication outages. Conditions are also given for the strong consistency of the parameter estimates. Simulation results provide an illustration of the algorithm properties. [ABSTRACT FROM AUTHOR]

This paper deals with recently proposed algorithms for real-time distributed blind macro-calibration of sensor networks based on consensus (synchronization). The algorithms are completely decentralized and do not require a fusion center. The goal is to consolidate all of the existing results on the subject, present them in a unified way, and provide additional important analysis of theoretical and practical issues that one can encounter when designing and applying the methodology. We first present the basic algorithm which estimates local calibration parameters by enforcing asymptotic consensus, in the mean-square sense and with probability one (w.p.1), on calibrated sensor gains and calibrated sensor offsets. For the more realistic case in which additive measurement noise, communication dropouts and additive communication noise are present, two algorithm modifications are discussed: one that uses a simple compensation term, and a more robust one based on an instrumental variable. The modified algorithms also achieve asymptotic agreement for calibrated sensor gains and offsets, in the mean-square sense and w.p.1. The convergence rate can be determined in terms of an upper bound on the mean-square error. The case when the communications between nodes is completely asynchronous, which is of substantial importance for real-world applications, is also presented. Suggestions for design of a priori adjustable weights are given. We also present the results for the case in which the underlying sensor network has a subset of (precalibrated) reference sensors with fixed calibration parameters. Wide applicability and efficacy of these algorithms are illustrated on several simulation examples. Finally, important open questions and future research directions are discussed. [ABSTRACT FROM AUTHOR]

In this paper we propose a novel stochastic consensus seeking algorithm based on the introduction of a nonlinear transformation aimed at robustification with respect to noise influence. The introduced nonlinear transformation is selected according to the methodology of stochastic approximation and robust statistics. The proposed algorithm represents a general nonlinear stochastic consensus seeking scheme, not yet treated in the literature. It provides a significant improvement over the linear algorithms from the point of view of robustness to noise, ensuring better convergence rate and lower sensitivity of the limit state value at consensus. One of the main contributions of the paper is the proof that the algorithm converges almost surely to consensus under general conditions. A detailed analysis of the limit state value at consensus is provided together with an insight into achievable convergence rate. Illustrative simulation results are also provided, demonstrating great advantages of the proposed algorithm compared to the existing consensus schemes. [ABSTRACT FROM AUTHOR]