## 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. |

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### 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 |

### Other editions - View all

Viability Theory: New Directions Jean-Pierre AUBIN,Alexandre M. Bayen,Patrick Saint-Pierre No preview available - 2011 |

### Common terms and phrases

associated assume Aubin auxiliary system backward invariant belongs boundary CaptS capture basin closed convex closed subset compact computed concept congestion function control system converges convex cone defined Definition denote derivatives differential inclusion Dirichlet boundary condition discrete domain dynamics environment epigraph equilibrium evolutionary system evolutions starting exists an evolution extended function feedback finite Frankowska graph Graph(U Hamilton–Jacobi Hamilton–Jacobi equation heavy evolution Hence implies inequality inertia function infimum Int(K intertemporal optimization interval invariance kernel inverse Julia set kernels and capture Lagrangian least one evolution Lemma Let us consider Limsup Lipschitz lower semicontinuous Lyapunov Lyapunov function map F Marchaud mathematical optimal evolutions parameters partial differential equation Proof Proposition R U oo regulation map regulons satisfying sequence set-valued map single-valued tangent cone Theorem trajectory tube tychastic upper semicompact value function vector space velocity viability and invariance viability constraints viability kernel viability solution viability theory viable evolutions ViabS ViabS(K