Viability Theory
Viability Theory

Author: Jean-Pierre Aubin

Publisher: Springer Science & Business Media

Published: 2011-07-13

Total Pages: 812

ISBN-13: 3642166849

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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.

Viability Theory
Viability Theory

Author: Jean-Pierre Aubin

Publisher: Springer Science & Business Media

Published: 2009-05-28

Total Pages: 558

ISBN-13: 0817649107

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"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 analysis...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 research...It gives a very thorough mathematical presentation. Very useful for anybody confronted with viability constraints." —Mededelingen van het Wiskundig Genootschap

Viability, Invariance and Applications
Viability, Invariance and Applications

Author: Ovidiu Carja

Publisher: Elsevier

Published: 2007-07-18

Total Pages: 357

ISBN-13: 0080521665

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The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time.The book includes the most important necessary and sufficient conditions for viability starting with Nagumo’s Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts. New concepts for multi-functions as the classical tangent vectors for functions Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions Clarifying examples, illustrations and numerous problems, completely and carefully solved Illustrates the applications from theory into practice Very clear and elegant style

Differential Inclusions
Differential Inclusions

Author: J.-P. Aubin

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 353

ISBN-13: 3642695124

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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

Viability and Resilience of Complex Systems
Viability and Resilience of Complex Systems

Author: Guillaume Deffuant

Publisher: Springer

Published: 2011-08-03

Total Pages: 227

ISBN-13: 3642204236

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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

Tychastic Measure of Viability Risk
Tychastic Measure of Viability Risk

Author: Jean-Pierre Aubin

Publisher: Springer

Published: 2014-08-06

Total Pages: 136

ISBN-13: 3319081292

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This book presents a forecasting mechanism of the price intervals for deriving the SCR (solvency capital requirement) eradicating the risk during the exercise period on one hand and measuring the risk by computing the hedging exit time function associating with smaller investments the date until which the value of the portfolio hedges the liabilities on the other. This information, summarized under the term “tychastic viability measure of risk” is an evolutionary alternative to statistical measures, when dealing with evolutions under uncertainty. The book is written by experts in the field and the target audience primarily comprises research experts and practitioners.

Viability of Hybrid Systems
Viability of Hybrid Systems

Author: G. Labinaz

Publisher: Springer Science & Business Media

Published: 2011-10-02

Total Pages: 250

ISBN-13: 9400725213

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The problem of viability of hybrid systems is considered in this work. A model for a hybrid system is developed including a means of including three forms of uncertainty: transition dynamics, structural uncertainty, and parametric uncertainty. A computational basis for viability of hybrid systems is developed and applied to three control law classes. An approach is developed for robust viability based on two extensions of the controllability operator. The three-tank example is examined for both the viability problem and robust viability problem. The theory is applied through simulation to an active magnetic bearing system and to a batch polymerization process showing that viability can be satisfied in practice. The problem of viable attainability is examined based on the controllability operator approach introduced by Nerode and colleagues. Lastly, properties of the controllability operator are presented.

Dynamic Economic Theory
Dynamic Economic Theory

Author: Jean-Pierre Aubin

Publisher: Springer

Published: 1997-05-20

Total Pages: 546

ISBN-13:

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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.

The Philosophy of Metacognition
The Philosophy of Metacognition

Author: Joëlle Proust

Publisher: OUP Oxford

Published: 2013-11-28

Total Pages: 379

ISBN-13: 0191662887

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Does metacognition, i.e. the capacity to form epistemic self-evaluations about one's current cognitive performance, derive from a mindreading capacity, or does it rely, at least in part, on sui generis informational processes? In The Philosophy of Metacognition Joëlle Proust provides a powerful defense of the second position. Drawing on discussions of empirical evidence from comparative, developmental, and experimental psychology, as well as from neuroscience, and on conceptual analyses, she purports to show that, in contrast with analytic metacognition, procedural metacognition does not need to involve metarepresentations. Procedural metacognition seems to be available to some non-humans (some primates and rodents). Proust further claims that metacognition is essentially related to mental agency, i.e. cognitive control and monitoring. 'Self-probing' is equivalent to a self-addressed question about the feasibility of a mental action ('Am I able to remember this word?'). 'Post-evaluating' is a way of asking oneself whether a given mental action has been successfully completed ('Is this word the one I was looking for?'). Neither question need be articulated conceptually for a feeling of knowing or of being right to be generated, or to drive epistemic control. Various issues raised by the contrast of a procedural, experience-based metacognition, with an analytic, concept-based metacognition are explored, such as whether each is expressed in a different representational format, their sensitivity to different epistemic norms, and the existence of a variety of types of epistemic acceptance.

Game Theory with Engineering Applications
Game Theory with Engineering Applications

Author: Dario Bauso

Publisher: SIAM

Published: 2016-02-29

Total Pages: 298

ISBN-13: 1611974275

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Engineering systems are highly distributed collective systems that have humans in the loop. Engineering systems emphasize the potential of control and games beyond traditional applications. Game theory can be used to design incentives to obtain socially desirable behaviors on the part of the players, for example, a change in the consumption patterns on the part of the ?prosumers? (producers-consumers) or better redistribution of traffic. This unique book addresses the foundations of game theory, with an emphasis on the physical intuition behind the concepts, an analysis of design techniques, and a discussion of new trends in the study of cooperation and competition in large complex distributed systems.?