73 research outputs found
Distributed Stochastic Optimization over Time-Varying Noisy Network
This paper is concerned with distributed stochastic multi-agent optimization
problem over a class of time-varying network with slowly decreasing
communication noise effects. This paper considers the problem in composite
optimization setting which is more general in noisy network optimization. It is
noteworthy that existing methods for noisy network optimization are Euclidean
projection based. We present two related different classes of non-Euclidean
methods and investigate their convergence behavior. One is distributed
stochastic composite mirror descent type method (DSCMD-N) which provides a more
general algorithm framework than former works in this literature. As a
counterpart, we also consider a composite dual averaging type method (DSCDA-N)
for noisy network optimization. Some main error bounds for DSCMD-N and DSCDA-N
are obtained. The trade-off among stepsizes, noise decreasing rates,
convergence rates of algorithm is analyzed in detail. To the best of our
knowledge, this is the first work to analyze and derive convergence rates of
optimization algorithm in noisy network optimization. We show that an optimal
rate of in nonsmooth convex optimization can be obtained for
proposed methods under appropriate communication noise condition. Moveover,
convergence rates in different orders are comprehensively derived in both
expectation convergence and high probability convergence sense.Comment: 27 page
Convergence Rate of a Message-passing Algorithm for Solving Linear Systems
This paper studies the convergence rate of a message-passing distributed
algorithm for solving a large-scale linear system. This problem is generalised
from the celebrated Gaussian Belief Propagation (BP) problem for statistical
learning and distributed signal processing, and this message-passing algorithm
is generalised from the well-celebrated Gaussian BP algorithm. Under the
assumption of generalised diagonal dominance, we reveal, through painstaking
derivations, several bounds on the convergence rate of the message-passing
algorithm. In particular, we show clearly how the convergence rate of the
algorithm can be explicitly bounded using the diagonal dominance properties of
the system. When specialised to the Gaussian BP problem, our work also offers
new theoretical insight into the behaviour of the BP algorithm because we use a
purely linear algebraic approach for convergence analysis
Event-Triggered Distributed Estimation With Decaying Communication Rate
We study distributed estimation of a high-dimensional static parameter vector
through a group of sensors whose communication network is modeled by a fixed
directed graph. Different from existing time-triggered communication schemes,
an event-triggered asynchronous scheme is investigated in order to reduce
communication while preserving estimation convergence. A distributed estimation
algorithm with a single step size is first proposed based on an event-triggered
communication scheme with a time-dependent decaying threshold. With the
event-triggered scheme, each sensor sends its estimate to neighbor sensors only
when the difference between the current estimate and the last sent-out estimate
is larger than the triggering threshold. Different sensors can have different
step sizes and triggering thresholds, enabling the parameter estimation process
to be conducted in a fully distributed way. We prove that the proposed
algorithm has mean-square and almost-sure convergence respectively, under
proper conditions of network connectivity and system collective observability.
The collective observability is the possibly mildest condition, since it is a
spatially and temporally collective condition of all sensors and allows sensor
observation matrices to be time-varying, stochastic, and non-stationary.
Moreover, we provide estimates for the convergence rates, which are related to
the step sizes as well as the triggering thresholds. Furthermore, we prove that
the communication rate is decaying to zero with a certain rate almost surely as
time goes to infinity. We show that it is feasible to tune the thresholds and
the step sizes such that requirements of algorithm convergence and
communication rate decay are satisfied simultaneously.Numerical simulations are
provided to illustrate the developed results
Distributed Randomized Gradient-Free Mirror Descent Algorithm for Constrained Optimization
This paper is concerned with multi-agent optimization problem. A distributed
randomized gradient-free mirror descent (DRGFMD) method is developed by
introducing a randomized gradient-free oracle in the mirror descent scheme
where the non-Euclidean Bregman divergence is used. The classical gradient
descent method is generalized without using subgradient information of
objective functions. The proposed algorithm is the first distributed
non-Euclidean zeroth-order method which achieves an convergence
rate, recovering the best known optimal rate of distributed compact constrained
convex optimization. Also, the DRGFMD algorithm achieves an
convergence rate for the strongly convex constrained optimization case. The
rate matches the best known non-compact constraint result. Moreover, a
decentralized reciprocal weighted average approximating sequence is
investigated and first used in distributed algorithm. A class of convergence
rates are also achieved for the algorithm with weighted averaging (DRGFMD-WA).
The technique on constructing the decentralized weighted average sequence
provides new insight in searching for minimizers in distributed algorithms.Comment: 14 pages, 6 figures, preprint submitted to IEEE TAC in November 201
Unknown Input Estimation Techniques in Networks and Applications to Open Channel Hydraulic Systems
This thesis is divided in two fundamental parts, namely, the Part I, in which the theoretical background of the UIO, Consensus Algorithms and Decentralized Systems is discussed; after a collection of algorithms is presented. In the Part II, some important applicative problems are
addressed and solved by means of the proposed approaches.
More specifically, as for the Part I, in Chapter 1 the fundamentals regarding the matrix and graph theory are recalled. In the subsequent Chapter 2 the attention is focused on the strong observability approach, and its main features are described. Chapter 3 refers to the presentation
of the Consensus algorithm, while in Chapter 4 an estimation algorithm is recalled, which allows the estimation of the state in an âoverlappedâ system also in presence of Unknown Inputs (in Chapter 5), which are estimated as well. In the Part II the estimation problems of flow ad infiltration, in open channel hydraulic sys-
tem are solved, using a UIO approach(in Chapters 6). In Chapters 7, considering open channel hydraulic system, the UIO approach is used to solve a problem of fault detection and compensation
Unknown Input Estimation Techniques in Networks and Applications to Open Channel Hydraulic Systems
This thesis is divided in two fundamental parts, namely, the Part I, in which the theoretical background of the UIO, Consensus Algorithms and Decentralized Systems is discussed; after a collection of algorithms is presented. In the Part II, some important applicative problems are
addressed and solved by means of the proposed approaches.
More specifically, as for the Part I, in Chapter 1 the fundamentals regarding the matrix and graph theory are recalled. In the subsequent Chapter 2 the attention is focused on the strong observability approach, and its main features are described. Chapter 3 refers to the presentation
of the Consensus algorithm, while in Chapter 4 an estimation algorithm is recalled, which allows the estimation of the state in an âoverlappedâ system also in presence of Unknown Inputs (in Chapter 5), which are estimated as well. In the Part II the estimation problems of flow ad infiltration, in open channel hydraulic sys-
tem are solved, using a UIO approach(in Chapters 6). In Chapters 7, considering open channel hydraulic system, the UIO approach is used to solve a problem of fault detection and compensation
Distributed Kalman Filters over Wireless Sensor Networks: Data Fusion, Consensus, and Time-Varying Topologies
Kalman filtering is a widely used recursive algorithm for optimal state estimation of linear stochastic dynamic systems. The recent advances of wireless sensor networks (WSNs) provide the technology to monitor and control physical processes with a high degree of temporal and spatial granularity. Several important problems concerning Kalman filtering over WSNs are addressed in this dissertation. First we study data fusion Kalman filtering for discrete-time linear time-invariant (LTI) systems over WSNs, assuming the existence of a data fusion center that receives observations from distributed sensor nodes and estimates the state of the target system in the presence of data packet drops. We focus on the single sensor node case and show that the critical data arrival rate of the Bernoulli channel can be computed by solving a simple linear matrix inequality problem. Then a more general scenario is considered where multiple sensor nodes are employed. We derive the stationary Kalman filter that minimizes the average error variance under a TCP-like protocol. The stability margin is adopted to tackle the stability issue. Second we study distributed Kalman filtering for LTI systems over WSNs, where each sensor node is required to locally estimate the state in a collaborative manner with its neighbors in the presence of data packet drops. The stationary distributed Kalman filter (DKF) that minimizes the local average error variance is derived. Building on the stationary DKF, we propose Kalman consensus filter for the consensus of different local estimates. The upper bound for the consensus coefficient is computed to ensure the mean square stability of the error dynamics. Finally we focus on time-varying topology. The solution to state consensus control for discrete-time homogeneous multi-agent systems over deterministic time-varying feedback topology is provided, generalizing the existing results. Then we study distributed state estimation over WSNs with time-varying communication topology. Under the uniform observability, each sensor node can closely track the dynamic state by using only its own observation, plus information exchanged with its neighbors, and carrying out local computation
Control Principles of Complex Networks
A reflection of our ultimate understanding of a complex system is our ability
to control its behavior. Typically, control has multiple prerequisites: It
requires an accurate map of the network that governs the interactions between
the system's components, a quantitative description of the dynamical laws that
govern the temporal behavior of each component, and an ability to influence the
state and temporal behavior of a selected subset of the components. With deep
roots in nonlinear dynamics and control theory, notions of control and
controllability have taken a new life recently in the study of complex
networks, inspiring several fundamental questions: What are the control
principles of complex systems? How do networks organize themselves to balance
control with functionality? To address these here we review recent advances on
the controllability and the control of complex networks, exploring the
intricate interplay between a system's structure, captured by its network
topology, and the dynamical laws that govern the interactions between the
components. We match the pertinent mathematical results with empirical findings
and applications. We show that uncovering the control principles of complex
systems can help us explore and ultimately understand the fundamental laws that
govern their behavior.Comment: 55 pages, 41 figures, Submitted to Reviews of Modern Physic
Dynamics and simulations of stochastic COVID-19 epidemic model using Legendre spectral collocation method
The aim of this study is to investigate the dynamics of epidemic transmission of COVID-19 SEIR stochastic model with generalized saturated incidence rate. We assume that the random perturbations depends on white noises, which implies that it is directly proportional to the steady states. The existence and uniqueness of the positive solution along with the stability analysis is provided under disease-free and endemic equilibrium conditions for asymptotically stable transmission dynamics of the model. An epidemiological metric based on the ratio of basic reproduction is used to describe the transmission of an infectious disease using different parameters values involve in the proposed model. A higher order scheme based on Legendre spectral collocation method is used for the numerical simulations. For the better understanding of the proposed scheme, a comparison is made with the deterministic counterpart. In order to confirm the theoretical analysis, we provide a number of numerical examples
Multi-Agent Systems
A multi-agent system (MAS) is a system composed of multiple interacting intelligent agents. Multi-agent systems can be used to solve problems which are difficult or impossible for an individual agent or monolithic system to solve. Agent systems are open and extensible systems that allow for the deployment of autonomous and proactive software components. Multi-agent systems have been brought up and used in several application domains
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