Viability Theory

New Directions
2. Auflage 2011
ISBN: 978-3-642-16683-9
Verlag: Springer

Buch, Englisch, 803 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1390 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Aubin, Jean-Pierre

Saint-Pierre, Patrick

Bayen, Alexandre M.

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften Interdisziplinär Naturwissenschaften, Technik, Medizin
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme

Inhaltsverzeichnis

Overview and Organization.- Viability Kernels and Examples: Viability and Capturability.- Viability Problems in Robotics.- Viability and Dynamic Intertemporal Optimality.- Avoiding Skylla and Charybdis.- Inertia Functions, Viability Oscillators and Hysteresis.- Management of Renewable Resources.- Mathematical Properties of Viability Kernels: Connection Basins.- Local and Asymptotic Properties of Equilibria.- Viability and Capturability Properties of Evolutionary Systems.- Regulation of Control Systems.- Restoring Viability.- First-Order Partial Differential Equations: Viability Solutions to Hamilton-Jacobi Equations.- Regulation of Traffic.- Illustrations in Finance and Economics.- Viability Solutions to Conservation Laws.- Viability Solutions to Hamilton-Jacobi-Bellman Equations.- Appendices: Set-Valued Analysis at a Glance.- Convergence and Viability Theorems.