Discrete Time Stochastic Control And Dynamic Potential Games
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Discrete–Time Stochastic Control and Dynamic Potential Games by David González-Sánchez,Onésimo Hernández-Lerma Pdf
There are several techniques to study noncooperative dynamic games, such as dynamic programming and the maximum principle (also called the Lagrange method). It turns out, however, that one way to characterize dynamic potential games requires to analyze inverse optimal control problems, and it is here where the Euler equation approach comes in because it is particularly well–suited to solve inverse problems. Despite the importance of dynamic potential games, there is no systematic study about them. This monograph is the first attempt to provide a systematic, self–contained presentation of stochastic dynamic potential games.
Stochastic Control in Discrete and Continuous Time by Atle Seierstad Pdf
This book contains an introduction to three topics in stochastic control: discrete time stochastic control, i. e. , stochastic dynamic programming (Chapter 1), piecewise - terministic control problems (Chapter 3), and control of Ito diffusions (Chapter 4). The chapters include treatments of optimal stopping problems. An Appendix - calls material from elementary probability theory and gives heuristic explanations of certain more advanced tools in probability theory. The book will hopefully be of interest to students in several ?elds: economics, engineering, operations research, ?nance, business, mathematics. In economics and business administration, graduate students should readily be able to read it, and the mathematical level can be suitable for advanced undergraduates in mathem- ics and science. The prerequisites for reading the book are only a calculus course and a course in elementary probability. (Certain technical comments may demand a slightly better background. ) As this book perhaps (and hopefully) will be read by readers with widely diff- ing backgrounds, some general advice may be useful: Don’t be put off if paragraphs, comments, or remarks contain material of a seemingly more technical nature that you don’t understand. Just skip such material and continue reading, it will surely not be needed in order to understand the main ideas and results. The presentation avoids the use of measure theory.
Potential Game Theory by Quang Duy Lã,Yong Huat Chew,Boon-Hee Soong Pdf
This book offers a thorough examination of potential game theory and its applications in radio resource management for wireless communications systems and networking. The book addresses two major research goals: how to identify a given game as a potential game, and how to design the utility functions and the potential functions with certain special properties in order to formulate a potential game. After proposing a unifying mathematical framework for the identification of potential games, the text surveys existing applications of this technique within wireless communications and networking problems found in OFDMA 3G/4G/WiFi networks, as well as next-generation systems such as cognitive radios and dynamic spectrum access networks. Professionals interested in understanding the theoretical aspect of this specialized field will find Potential Game Theory a valuable resource, as will advanced-level engineering students. It paves the way for extensive and rigorous research exploration on a topic whose capacity for practical applications is vast but not yet fully exploited.
Mathematical Optimization Theory and Operations Research by Michael Khachay,Yury Kochetov,Panos Pardalos Pdf
This book constitutes the proceedings of the 18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019, held in Ekaterinburg, Russia, in July 2019. The 48 full papers presented in this volume were carefully reviewed and selected from 170 submissions. MOTOR 2019 is a successor of the well-known International and All-Russian conference series, which were organized in Ural, Siberia, and the Far East for a long time. The selected papers are organized in the following topical sections: mathematical programming; bi-level optimization; integer programming; combinatorial optimization; optimal control and approximation; data mining and computational geometry; games and mathematical economics.
Optimization, Control, and Applications of Stochastic Systems by Daniel Hernández-Hernández,J. Adolfo Minjárez-Sosa Pdf
This volume provides a general overview of discrete- and continuous-time Markov control processes and stochastic games, along with a look at the range of applications of stochastic control and some of its recent theoretical developments. These topics include various aspects of dynamic programming, approximation algorithms, and infinite-dimensional linear programming. In all, the work comprises 18 carefully selected papers written by experts in their respective fields. Optimization, Control, and Applications of Stochastic Systems will be a valuable resource for all practitioners, researchers, and professionals in applied mathematics and operations research who work in the areas of stochastic control, mathematical finance, queueing theory, and inventory systems. It may also serve as a supplemental text for graduate courses in optimal control and dynamic games.
Optimal Control of Stochastic Difference Volterra Equations by Leonid Shaikhet Pdf
This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools. The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations. Optimal Control of Stochastic Difference Volterra Equations commences with an historical introduction to the emergence of this type of equation with some additional mathematical preliminaries. It then deals with the necessary conditions for optimality in the control of the equations and constructs a feedback control scheme. The approximation of stochastic quasilinear Volterra equations with quadratic performance functionals is then considered. Optimal stabilization is discussed and the filtering problem formulated. Finally, two methods of solving the optimal control problem for partly observable linear stochastic processes, also with quadratic performance functionals, are developed. Integrating the author’s own research within the context of the current state-of-the-art of research in difference equations, hereditary systems theory and optimal control, this book is addressed to specialists in mathematical optimal control theory and to graduate students in pure and applied mathematics and control engineering.
Discrete Gambling and Stochastic Games by Ashok P. Maitra,William Sudderth Pdf
The theory of probability began in the seventeenth century with attempts to calculate the odds of winning in certain games of chance. However, it was not until the middle of the twentieth century that mathematicians de veloped general techniques for maximizing the chances of beating a casino or winning against an intelligent opponent. These methods of finding op timal strategies for a player are at the heart of the modern theories of stochastic control and stochastic games. There are numerous applications to engineering and the social sciences, but the liveliest intuition still comes from gambling. The now classic work How to Gamble If You Must: Inequalities for Stochastic Processes by Dubins and Savage (1965) uses gambling termi nology and examples to develop an elegant, deep, and quite general theory of discrete-time stochastic control. A gambler "controls" the stochastic pro cess of his or her successive fortunes by choosing which games to play and what bets to make.
Stochastic Optimal Control: The Discrete-Time Case by Dimitri Bertsekas,Steven E. Shreve Pdf
This research monograph, first published in 1978 by Academic Press, remains the authoritative and comprehensive treatment of the mathematical foundations of stochastic optimal control of discrete-time systems, including the treatment of the intricate measure-theoretic issues. It is an excellent supplement to the first author's Dynamic Programming and Optimal Control (Athena Scientific, 2018). Review of the 1978 printing:"Bertsekas and Shreve have written a fine book. The exposition is extremely clear and a helpful introductory chapter provides orientation and a guide to the rather intimidating mass of literature on the subject. Apart from anything else, the book serves as an excellent introduction to the arcane world of analytic sets and other lesser known byways of measure theory." Mark H. A. Davis, Imperial College, in IEEE Trans. on Automatic Control Among its special features, the book: 1) Resolves definitively the mathematical issues of discrete-time stochastic optimal control problems, including Borel models, and semi-continuous models 2) Establishes the most general possible theory of finite and infinite horizon stochastic dynamic programming models, through the use of analytic sets and universally measurable policies 3) Develops general frameworks for dynamic programming based on abstract contraction and monotone mappings 4) Provides extensive background on analytic sets, Borel spaces and their probability measures 5) Contains much in depth research not found in any other textbook
Finite Approximations in Discrete-Time Stochastic Control by Naci Saldi,Tamás Linder,Serdar Yüksel Pdf
In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original models and the methods are general enough that researchers can build corresponding approximation results, typically with no additional assumptions.
Techniques in Discrete-Time Stochastic Control Systems by Anonim Pdf
Praise for Previous Volumes "This book will be a useful reference to control engineers and researchers. The papers contained cover well the recent advances in the field of modern control theory." -IEEE GROUP CORRESPONDANCE "This book will help all those researchers who valiantly try to keep abreast of what is new in the theory and practice of optimal control." -CONTROL
Neural Approximations for Optimal Control and Decision by Riccardo Zoppoli,Marcello Sanguineti,Giorgio Gnecco,Thomas Parisini Pdf
Neural Approximations for Optimal Control and Decision provides a comprehensive methodology for the approximate solution of functional optimization problems using neural networks and other nonlinear approximators where the use of traditional optimal control tools is prohibited by complicating factors like non-Gaussian noise, strong nonlinearities, large dimension of state and control vectors, etc. Features of the text include: • a general functional optimization framework; • thorough illustration of recent theoretical insights into the approximate solutions of complex functional optimization problems; • comparison of classical and neural-network based methods of approximate solution; • bounds to the errors of approximate solutions; • solution algorithms for optimal control and decision in deterministic or stochastic environments with perfect or imperfect state measurements over a finite or infinite time horizon and with one decision maker or several; • applications of current interest: routing in communications networks, traffic control, water resource management, etc.; and • numerous, numerically detailed examples. The authors’ diverse backgrounds in systems and control theory, approximation theory, machine learning, and operations research lend the book a range of expertise and subject matter appealing to academics and graduate students in any of those disciplines together with computer science and other areas of engineering.
Optimal Control and Dynamic Games by Christophe Deissenberg,Richard F. Hartl Pdf
Optimal Control and Dynamic Games has been edited to honor the outstanding contributions of Professor Suresh Sethi in the fields of Applied Optimal Control. Professor Sethi is internationally one of the foremost experts in this field. He is, among others, co-author of the popular textbook "Sethi and Thompson: Optimal Control Theory: Applications to Management Science and Economics". The book consists of a collection of essays by some of the best known scientists in the field, covering diverse aspects of applications of optimal control and dynamic games to problems in Finance, Management Science, Economics, and Operations Research. In doing so, it provides both a state-of-the-art overview over recent developments in the field, and a reference work covering the wide variety of contemporary questions that can be addressed with optimal control tools, and demonstrates the fruitfulness of the methodology.
