Viability Theory: New DirectionsViability 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. |
Contents
1 | |
Part I Viability Kernels and Examples | 42 |
Part II Mathematical Properties of Viability Kernels | 272 |
Part III FirstOrder Partial Differential Equations | 521 |
Part IV Appendices | 712 |
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Viability Theory: New Directions Jean-Pierre Aubin,Alexandre M. Bayen,Patrick Saint-Pierre No preview available - 2011 |
Common terms and phrases
algorithm allows associated assume assumptions auxiliary backward belongs boundary called capture basin chapter Characterization closed compact computed concept condition cone congestion Consequently constant constraints contained continuous control system converges convex defined Definition denote depend derivatives differential inclusion discrete domain dynamics economic elements environment epigraph equal equilibrium equivalent evolution evolutionary system example exists exit extended finite formula function given governed graph Graph(U Hence implies inequality inertia function initial interval introduce invariant inverse least Lemma Let us consider limit lower semicontinuous Marchaud mathematical means measure minimal observe obtain optimal pair partial differential equation positive problem Proof Proposition prove reaches regarded regulation map regulons remains satisfying sense sequence set-valued map space starting subset taking tangent target Theorem traffic tube unique upper value function viability kernel viability solution viability theory viable evolutions ViabS(K