Multitask Diffusion Adaptation over Networks

Adaptive networks are suitable for decentralized inference tasks, e.g., to monitor complex natural phenomena. Recent research works have intensively studied distributed optimization problems in the case where the nodes have to estimate a single optimum parameter vector collaboratively. However, there are many important applications that are multitask-oriented in the sense that there are multiple optimum parameter vectors to be inferred simultaneously, in a collaborative manner, over the area covered by the network. In this paper, we employ diffusion strategies to develop distributed algorithms that address multitask problems by minimizing an appropriate mean-square error criterion with $\ell_2$-regularization. The stability and convergence of the algorithm in the mean and in the mean-square sense is analyzed. Simulations are conducted to verify the theoretical findings, and to illustrate how the distributed strategy can be used in several useful applications related to spectral sensing, target localization, and hyperspectral data unmixing.Comment: 29 pages, 11 figures, submitted for publicatio

Learning and Prediction Theory of Distributed Least Squares

With the fast development of the sensor and network technology, distributed estimation has attracted more and more attention, due to its capability in securing communication, in sustaining scalability, and in enhancing safety and privacy. In this paper, we consider a least-squares (LS)-based distributed algorithm build on a sensor network to estimate an unknown parameter vector of a dynamical system, where each sensor in the network has partial information only but is allowed to communicate with its neighbors. Our main task is to generalize the well-known theoretical results on the traditional LS to the current distributed case by establishing both the upper bound of the accumulated regrets of the adaptive predictor and the convergence of the distributed LS estimator, with the following key features compared with the existing literature on distributed estimation: Firstly, our theory does not need the previously imposed independence, stationarity or Gaussian property on the system signals, and hence is applicable to stochastic systems with feedback control. Secondly, the cooperative excitation condition introduced and used in this paper for the convergence of the distributed LS estimate is the weakest possible one, which shows that even if any individual sensor cannot estimate the unknown parameter by the traditional LS, the whole network can still fulfill the estimation task by the distributed LS. Moreover, our theoretical analysis is also different from the existing ones for distributed LS, because it is an integration of several powerful techniques including stochastic Lyapunov functions, martingale convergence theorems, and some inequalities on convex combination of nonnegative definite matrices.Comment: 14 pages, submitted to IEEE Transactions on Automatic Contro

Distributed Least Squares Algorithm for Continuous-time Stochastic Systems Under Cooperative Excitation Condition

In this paper, we study the distributed adaptive estimation problem of continuous-time stochastic dynamic systems over sensor networks where each agent can only communicate with its local neighbors. A distributed least squares (LS) algorithm based on diffusion strategy is proposed such that the sensors can cooperatively estimate the unknown time-invariant parameter vector from continuous-time noisy signals. By using the martingal estimation theory and Ito formula, we provide upper bounds for the estimation error of the proposed distributed LS algorithm, and further obtain the convergence results under a cooperative excitation condition. Compared with the existing results, our results are established without using the boundedness or persistent excitation (PE) conditions of regression signals. We provide simulation examples to show that multiple sensors can cooperatively accomplish the estimation task even if any individual can not

Learning for informative path planning

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 104-108).Through the combined use of regression techniques, we will learn models of the uncertainty propagation efficiently and accurately to replace computationally intensive Monte- Carlo simulations in informative path planning. This will enable us to decrease the uncertainty of the weather estimates more than current methods by enabling the evaluation of many more candidate paths given the same amount of resources. The learning method and the path planning method will be validated by the numerical experiments using the Lorenz-2003 model [32], an idealized weather model.by Sooho Park.S.M

Stochastic Algorithms in Riemannian Manifolds and Adaptive Networks

The combination of adaptive network algorithms and stochastic geometric dynamics has the potential to make a large impact in distributed control and signal processing applications. However, both literatures contain fundamental unsolved problems. The thesis is thus in two main parts. In part I, we consider stochastic differential equations (SDEs) evolving in a matrix Lie group. To undertake any kind of statistical signal processing or control task in this setting requires the simulation of such geometric SDEs. This foundational issue has barely been addressed previously. Chapter 1 contains background and motivation. Chapter 2 develops numerical schemes for simulating SDEs that evolve in SO(n) and SE(n). We propose novel, reliable, efficient schemes based on diagonal Padé approximants, where each trajectory lies in the respective manifold. We prove first order convergence in mean uniform squared error using a new proof technique. Simulations for SDEs in SO(50) are provided. In part II, we study adaptive networks. These are collections of individual agents (nodes) that cooperate to solve estimation, detection, learning and adaptation problems in real time from streaming data, without a fusion center. We study general diffusion LMS algorithms - including real time consensus - for distributed MMSE parameter estimation. This choice is motivated by two major flaws in the literature. First, all analyses assume the regressors are white noise, whereas in practice serial correlation is pervasive. Dealing with it however is much harder than the white noise case. Secondly, since the algorithms operate in real time, we must consider realization-wise behavior. There are no such results. To remedy these flaws, we uncover the mixed time scale structure of the algorithms. We then perform a novel mixed time scale stochastic averaging analysis. Chapter 3 contains background and motivation. Realization-wise stability (chapter 4) and performance including network MSD, EMSE and realization-wise fluctuations (chapter 5) are then studied. We develop results in the difficult but realistic case of serial correlation. We observe that the popular ATC, CTA and real time consensus algorithms are remarkably similar in terms of stability and performance for small constant step sizes. Parts III and IV contain conclusions and future work

Application of Power Electronics Converters in Smart Grids and Renewable Energy Systems

This book focuses on the applications of Power Electronics Converters in smart grids and renewable energy systems. The topics covered include methods to CO2 emission control, schemes for electric vehicle charging, reliable renewable energy forecasting methods, and various power electronics converters. The converters include the quasi neutral point clamped inverter, MPPT algorithms, the bidirectional DC-DC converter, and the push–pull converter with a fuzzy logic controller