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Author: Jean Pierre Aubin Publisher: ISBN: Category : Differential inclusions Languages : en Pages : 584
Book Description
This work examines viability theory and its applications to control theory and differential games. The emphasis is on the construction of feedbacks and dynamical systems by myopic optimization methods. Systems of first-order partial differential inclusions, whose solutions are feedbacks, are constructed and investigated. Basic results are then extended to the case of fuzzy control problems, distributed control problems, and control systems with delays and memory. Aimed at graduate students and research mathematicians, both pure and applied, this book offers specialists in control and nonlinear systems tools to take into account general state constraints. Viability theory also allows researchers in other disciplinesâartificial intelligence, economics, game theory, theoretical biology, population genetics, cognitive sciencesâto go beyond deterministic models by studying them in a dynamical or evolutionary perspective in an uncertain environment. "The book is a compendium of the state of knowledge about viability...Mathematically, the book should be accessible to anyone who has had basic graduate courses in modern analysis and functional analysisâ¦The concepts are defined and many proofs of the requisite results are reproduced here, making the present book essentially self-contained." (Bulletin of the AMS) "Because of the wide scope, the book is an ideal reference for people encountering problems related to viability theory in their researchâ¦It gives a very thorough mathematical presentation. Very useful for anybody confronted with viability constraints." (Mededelingen van het Wiskundig Genootschap)
Author: Jean Pierre Aubin Publisher: ISBN: Category : Differential inclusions Languages : en Pages : 584
Book Description
This work examines viability theory and its applications to control theory and differential games. The emphasis is on the construction of feedbacks and dynamical systems by myopic optimization methods. Systems of first-order partial differential inclusions, whose solutions are feedbacks, are constructed and investigated. Basic results are then extended to the case of fuzzy control problems, distributed control problems, and control systems with delays and memory. Aimed at graduate students and research mathematicians, both pure and applied, this book offers specialists in control and nonlinear systems tools to take into account general state constraints. Viability theory also allows researchers in other disciplinesâartificial intelligence, economics, game theory, theoretical biology, population genetics, cognitive sciencesâto go beyond deterministic models by studying them in a dynamical or evolutionary perspective in an uncertain environment. "The book is a compendium of the state of knowledge about viability...Mathematically, the book should be accessible to anyone who has had basic graduate courses in modern analysis and functional analysisâ¦The concepts are defined and many proofs of the requisite results are reproduced here, making the present book essentially self-contained." (Bulletin of the AMS) "Because of the wide scope, the book is an ideal reference for people encountering problems related to viability theory in their researchâ¦It gives a very thorough mathematical presentation. Very useful for anybody confronted with viability constraints." (Mededelingen van het Wiskundig Genootschap)
Author: Jean-Pierre Aubin Publisher: Springer Science & Business Media ISBN: 3642166849 Category : Science Languages : en Pages : 812
Book Description
Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory, explaining and motivating the main concepts and illustrating them with numerous numerical examples taken from various fields.
Author: J.-P. Aubin Publisher: Springer Science & Business Media ISBN: 3642695124 Category : Mathematics Languages : en Pages : 353
Book Description
A great impetus to study differential inclusions came from the development of Control Theory, i.e. of dynamical systems x'(t) = f(t, x(t), u(t)), x(O)=xo "controlled" by parameters u(t) (the "controls"). Indeed, if we introduce the set-valued map F(t, x)= {f(t, x, u)}ueu then solutions to the differential equations (*) are solutions to the "differen tial inclusion" (**) x'(t)EF(t, x(t)), x(O)=xo in which the controls do not appear explicitely. Systems Theory provides dynamical systems of the form d x'(t)=A(x(t)) dt (B(x(t))+ C(x(t)); x(O)=xo in which the velocity of the state of the system depends not only upon the x(t) of the system at time t, but also on variations of observations state B(x(t)) of the state. This is a particular case of an implicit differential equation f(t, x(t), x'(t)) = 0 which can be regarded as a differential inclusion (**), where the right-hand side F is defined by F(t, x)= {vlf(t, x, v)=O}. During the 60's and 70's, a special class of differential inclusions was thoroughly investigated: those of the form X'(t)E - A(x(t)), x (0) =xo where A is a "maximal monotone" map. This class of inclusions contains the class of "gradient inclusions" which generalize the usual gradient equations x'(t) = -VV(x(t)), x(O)=xo when V is a differentiable "potential". 2 Introduction There are many instances when potential functions are not differentiable
Author: Guillaume Deffuant Publisher: Springer Science & Business Media ISBN: 3642204228 Category : Social Science Languages : en Pages : 227
Book Description
One common characteristics of a complex system is its ability to withstand major disturbances and the capacity to rebuild itself. Understanding how such systems demonstrate resilience by absorbing or recovering from major external perturbations requires both quantitative foundations and a multidisciplinary view on the topic. This book demonstrates how new methods can be used to identify the actions favouring the recovery from perturbations. Examples discussed include bacterial biofilms resisting detachment, grassland savannahs recovering from fire, the dynamics of language competition and Internet social networking sites overcoming vandalism. The reader is taken through an introduction to the idea of resilience and viability and shown the mathematical basis of the techniques used to analyse systems. The idea of individual or agent-based modelling of complex systems is introduced and related to analytically tractable approximations of such models. A set of case studies illustrates the use of the techniques in real applications, and the final section describes how one can use new and elaborate software tools for carrying out the necessary calculations. The book is intended for a general scientific audience of readers from the natural and social sciences, yet requires some mathematics to gain a full understanding of the more theoretical chapters. It is an essential point of reference for those interested in the practical application of the concepts of resilience and viability
Author: Jean-Pierre Aubin Publisher: Springer ISBN: 9783642645426 Category : Business & Economics Languages : en Pages : 510
Book Description
This book is intended to provide economists with mathematical tools necessary to handle the concepts of evolution under uncertainty and adaption arising in economics, pursuing the Arrow-Debreu-Hahn legacy. It applies the techniques of viability theory to the study of economic systems evolving under contingent uncertainty, faced with scarcity constraints, and obeying various implementation of the inertia principle. The book illustrates how new tools can be used to move from static analysis, built on concepts of optima, equilibria and attractors to a contingent dynamic framework.
Author: William F. Morris Publisher: Sinauer Associates Incorporated ISBN: 9780878935468 Category : Science Languages : en Pages : 480
Book Description
The goal of this book is to provide practical, intelligible, and intuitive explanations of population modelling to empirical ecologists and conservation biologists. Modelling methods that do not require large amounts of data (typically unavailable for endangered species) are emphasised. As such, the book is appropriate for undergraduate and graduate students interested in quantitative conservation biology, managers charged with preserving endangered species, and, in short, for any conservation biologist or ecologist seeking to better understand the analysis and modelling of population data.
Author: Girol Karacaoglu Publisher: Springer ISBN: 9811361045 Category : Political Science Languages : en Pages : 257
Book Description
The distinctive contribution of this book is the formulation of an integrated social, environmental, and economic framework for public policy. This contribution is realised through investigations and conclusions in the following four domains: a formal stylised model that provides a platform for an integrated approach to public policy; a policy-informing simulation model that can be used to operationalise the public policy insights proposed in the stylised model; the implications of introducing fundamental (or radical) uncertainty and complexity into the policy framework; and the use of viability theory to demonstrate how one can think of and implement public policy in an uncertain and complex world, when the focus of policy needs to shift to building resilience to systemic risks. The book’s stylised model is constructed by weaving together threads from the wellbeing, human needs, complex systems, sustainable development, endogenous economic growth, directed technical change, and credit-based-money literatures. Throughout, the perspective is that of a policy adviser to a "wellbeing state", as distinct from a "welfare state". The key linkages or relationships in the model are supported by empirical evidence that draws on the wider literature in related fields.
Author: Steven R. Beissinger Publisher: University of Chicago Press ISBN: 0226041786 Category : Nature Languages : en Pages : 594
Book Description
Many of the world's leading conservation and population biologists evaluate what has become a key tool in estimating extinction risk and evaluating potential recovery strategies - population viability analysis, or PVA.
Author: Jean-Pierre Aubin Publisher: Cambridge University Press ISBN: 9780521445320 Category : Computers Languages : en Pages : 306
Book Description
This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded as dynamical systems controlled by synaptic matrices, and set-valued analysis that plays a natural and crucial role in qualitative analysis and simulation. This allows many examples of neural networks to be presented in a unified way. In addition, several results on the control of linear and nonlinear systems are used to obtain a "learning algorithm" of pattern classification problems, such as the back-propagation formula, as well as learning algorithms of feedback regulation laws of solutions to control systems subject to state constraints.
Author: Richard Dawid Publisher: Cambridge University Press ISBN: 1107067588 Category : Science Languages : en Pages : 213
Book Description
String theory has played a highly influential role in theoretical physics for nearly three decades and has substantially altered our view of the elementary building principles of the Universe. However, the theory remains empirically unconfirmed, and is expected to remain so for the foreseeable future. So why do string theorists have such a strong belief in their theory? This book explores this question, offering a novel insight into the nature of theory assessment itself. Dawid approaches the topic from a unique position, having extensive experience in both philosophy and high-energy physics. He argues that string theory is just the most conspicuous example of a number of theories in high-energy physics where non-empirical theory assessment has an important part to play. Aimed at physicists and philosophers of science, the book does not use mathematical formalism and explains most technical terms.
Author: Jean Pierre Aubin
Author: Jean Pierre Aubin
Author: Jean-Pierre Aubin
Author: J.-P. Aubin
Author: Guillaume Deffuant
Author: Jean-Pierre Aubin
Author: William F. Morris
Author: Girol Karacaoglu
Author: Steven R. Beissinger
Author: Jean-Pierre Aubin
Author: Richard Dawid