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Author: Thu Thi Le Nguyen
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 103
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Book Description
The second part studies general stochastic approximation algorithms with switching which include many applications that had appeared on literature as special cases. We investigate the inherent interaction between control and communication systems by considering classes SA algorithms that accommodate random network topology, nonlinear dynamics, with complex system noise structures (additive or non additive), and other uncertainties in a unified framework. Interaction among control strategy and the multiple stochastic processes introduces critical challenges in such problems. By modeling the random switching as a discrete time Markov chain and studying multiple stochastic uncertainties in a unified framework, it is shown that under broad conditions, the algorithms are convergent. The performance of the algorithms is further analyzed by establishing their rate of convergence and asymptotic characterizations. Simulation case studies are conducted to evaluate the performance of the procedures in various aspects.
Author: Thu Thi Le Nguyen
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 103
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Book Description
The second part studies general stochastic approximation algorithms with switching which include many applications that had appeared on literature as special cases. We investigate the inherent interaction between control and communication systems by considering classes SA algorithms that accommodate random network topology, nonlinear dynamics, with complex system noise structures (additive or non additive), and other uncertainties in a unified framework. Interaction among control strategy and the multiple stochastic processes introduces critical challenges in such problems. By modeling the random switching as a discrete time Markov chain and studying multiple stochastic uncertainties in a unified framework, it is shown that under broad conditions, the algorithms are convergent. The performance of the algorithms is further analyzed by establishing their rate of convergence and asymptotic characterizations. Simulation case studies are conducted to evaluate the performance of the procedures in various aspects.
Author: Harold Kushner
Publisher: Springer
ISBN: 9781441918475
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a thorough revision, although the main features and structure remain unchanged. It contains many additional applications and results as well as more detailed discussion.
Author: Hanfu Chen
Publisher: Springer Science & Business Media
ISBN: 9781402008061
Category : Language Arts & Disciplines
Languages : en
Pages : 384
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Book Description
Estimating unknown parameters based on observation data conta- ing information about the parameters is ubiquitous in diverse areas of both theory and application. For example, in system identification the unknown system coefficients are estimated on the basis of input-output data of the control system; in adaptive control systems the adaptive control gain should be defined based on observation data in such a way that the gain asymptotically tends to the optimal one; in blind ch- nel identification the channel coefficients are estimated using the output data obtained at the receiver; in signal processing the optimal weighting matrix is estimated on the basis of observations; in pattern classifi- tion the parameters specifying the partition hyperplane are searched by learning, and more examples may be added to this list. All these parameter estimation problems can be transformed to a root-seeking problem for an unknown function. To see this, let - note the observation at time i. e. , the information available about the unknown parameters at time It can be assumed that the parameter under estimation denoted by is a root of some unknown function This is not a restriction, because, for example, may serve as such a function.
Author: Harold Joseph Kushner
Publisher: MIT Press
ISBN: 9780262110907
Category : Computers
Languages : en
Pages : 296
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Book Description
Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and methods for random processes and applies them to numerous problems of practical importance. In particular, it develops usable and broad conditions and techniques for showing that a sequence of processes converges to a Markov diffusion or jump process. This is useful when the natural physical model is quite complex, in which case a simpler approximation la diffusion process, for example) is usually made. The book simplifies and extends some important older methods and develops some powerful new ones applicable to a wide variety of limit and approximation problems. The theory of weak convergence of probability measures is introduced along with general and usable methods (for example, perturbed test function, martingale, and direct averaging) for proving tightness and weak convergence. Kushner's study begins with a systematic development of the method. It then treats dynamical system models that have state-dependent noise or nonsmooth dynamics. Perturbed Liapunov function methods are developed for stability studies of nonMarkovian problems and for the study of asymptotic distributions of non-Markovian systems. Three chapters are devoted to applications in control and communication theory (for example, phase-locked loops and adoptive filters). Smallnoise problems and an introduction to the theory of large deviations and applications conclude the book. Harold J. Kushner is Professor of Applied Mathematics and Engineering at Brown University and is one of the leading researchers in the area of stochastic processes concerned with analysis and synthesis in control and communications theory. This book is the sixth in The MIT Press Series in Signal Processing, Optimization, and Control, edited by Alan S. Willsky.
Author: Lennart Ljung
Publisher: Birkhauser
ISBN:
Category : Mathematics
Languages : en
Pages : 132
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Book Description
Author: George Yin
Publisher: Springer
ISBN: 3030254984
Category : Mathematics
Languages : en
Pages : 599
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Book Description
This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.
Author: Harold Kushner
Publisher: Springer Science & Business Media
ISBN: 1489926968
Category : Mathematics
Languages : en
Pages : 432
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Book Description
The most comprehensive and thorough treatment of modern stochastic approximation type algorithms to date, based on powerful methods connected with that of the ODE. It covers general constrained and unconstrained problems, w.p.1 as well as the very successful weak convergence methods under weak conditions on the dynamics and noise processes, asymptotic properties and rates of convergence, iterate averaging methods, ergodic cost problems, state dependent noise, high dimensional problems, plus decentralized and asynchronous algorithms, and the use of methods of large deviations. Examples from many fields illustrate and motivate the techniques.
Author: Michael Neely
Publisher: Springer Nature
ISBN: 303179995X
Category : Computers
Languages : en
Pages : 199
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Book Description
This text presents a modern theory of analysis, control, and optimization for dynamic networks. Mathematical techniques of Lyapunov drift and Lyapunov optimization are developed and shown to enable constrained optimization of time averages in general stochastic systems. The focus is on communication and queueing systems, including wireless networks with time-varying channels, mobility, and randomly arriving traffic. A simple drift-plus-penalty framework is used to optimize time averages such as throughput, throughput-utility, power, and distortion. Explicit performance-delay tradeoffs are provided to illustrate the cost of approaching optimality. This theory is also applicable to problems in operations research and economics, where energy-efficient and profit-maximizing decisions must be made without knowing the future. Topics in the text include the following: - Queue stability theory - Backpressure, max-weight, and virtual queue methods - Primal-dual methods for non-convex stochastic utility maximization - Universal scheduling theory for arbitrary sample paths - Approximate and randomized scheduling theory - Optimization of renewal systems and Markov decision systems Detailed examples and numerous problem set questions are provided to reinforce the main concepts. Table of Contents: Introduction / Introduction to Queues / Dynamic Scheduling Example / Optimizing Time Averages / Optimizing Functions of Time Averages / Approximate Scheduling / Optimization of Renewal Systems / Conclusions
Author: Sina Firouzabadi
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
This thesis investigates different stochastic approximation-based algorithms for performance optimization of wireless networks. Stochastic approximation is used to learn the randomly-varying characteristics of the network conditions and adapt the transmission strategies accordingly. The basic premise of wireless network optimization based on stochastic approximation will be presented, followed by several applications of this technique. The first application optimizes secondary user transmission strategies in cognitive networks with imperfect network state observations. In this setting the secondary user maximizes its revenue while generating a bounded performance loss to the primary users' network. The state of the primary users' network, defined as a collection of variables describing features of the network (e.g., buffer state, packet service state) evolves over time according to a homogeneous Markov process. The statistics of the Markov process are dependent on the strategy of the secondary user and, thus, the instantaneous idleness/transmission action of the secondary user has a long term impact on the temporal evolution of the network. The Markov process generates a sequence of states in the state space of the network that projects onto a sequence of observations in the observation space, that is, the collection of all the observations of the secondary user. Based on the sequence of observations from secondary users, an iterative stochastic approximation based algorithm is proposed that optimizes the strategy of the secondary users with no a priori knowledge of the statistics of the Markov process and of the state-observation probability map. The second application of stochastic approximation theory presented is around the design of green cellular networks through the use of distributed antennas. After presenting an information theoretic analysis of the ergodic capacity of distributed antenna systems in a cellular setting, optimized antenna placement in such systems is investigated. A general framework for this optimization based on stochastic approximation theory, with no constraint on the location of the antennas, will be presented. It will be shown that optimal placement of antennas inside the coverage region can significantly improve the power efficiency of wireless networks. As we will see, our stochastic optimization framework is sufficiently general to incorporate interference as well as general performance metrics. We will also present different numerical studies for illustrating the power efficiency and area spectral efficiency of distributed antenna systems, under different assumptions about availability of channel side information at the transmitter. Finally in the last part of the thesis, we present a distributed algorithm for optimizing the rate-reliability tradeoff in wireless networks with randomly time-varying channels. The stochastic optimization is based on wireless network utility maximization, extended to incorporate dynamics at the physical layer. The proposed algorithm enables a distributed implementation. We also verify the convergence of the proposed algorithm using Stochastic Approximation. The performance of the proposed algorithm and its convergence is illustrated via simulations.
Author: Vivek S. Borkar
Publisher:
ISBN: 9788195196111
Category : Artificial intelligence
Languages : en
Pages : 0
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Book Description
This book serves as an advanced text for a graduate course on stochastic algorithms for graduate students in probability and statistics, engineering, economics and machine learning. This second edition gives a comprehensive treatment of stochastic approximation algorithms based on the ordinary differential equation (ODE) approach which analyses the algorithm in terms of a limiting ODE. It has a streamlined treatment of the classical convergence analysis and includes several recent developments such as concentration bounds, avoidance of traps, stability tests, distributed and asynchronous schemes, multiple time scales, general noise models, etc., and a category-wise exposition of many important applications. It is also a useful reference for researchers and practitioners in the field.
