Neural Networks and Qualitative Physics: A Viability Approach

By Jean-Pierre Aubin

Book Overview

This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded as dynamical systems controlled by synaptic matrices, and set-valued analysis that plays a natural and crucial role in qualitative analysis and simulation. This allows many examples of neural networks to be presented in a unified way. In addition, several results on the control of linear and nonlinear systems are used to obtain a "learning algorithm" of pattern classification problems, such as the back-propagation formula, as well as learning algorithms of feedback regulation laws of solutions to control systems subject to state constraints.

• Format: Paperback
• Language: English
• ISBN: 1107402840
• ISBN13: 9781107402843
• Release Date: August 2011
• Publisher: Cambridge University Press
• Length: 302 Pages
• Weight: 0.89 lbs.
• Dimensions: 0.6" x 6.0" x 9.0"