Viability Theory New Directions /

• Main Authors: Aubin, Jean-Pierre (Author), Bayen, Alexandre M. (Author), Saint-Pierre, Patrick (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Subjects: Mathematics.; Computer science > Mathematics.; Game theory.; System theory.; Control engineering.; Economic theory.; Systems Theory, Control.; Economic Theory/Quantitative Economics/Mathematical Methods.; Math Applications in Computer Science.; Control.; Game Theory, Economics, Social and Behav. Sciences.

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 enviro...

Table of Contents:

• 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.