Nonlinear Analysis, Differential Equations and Control

by Clarke, Frank H.; Stern, R. J.; Sabidussi, G.

• ISBN13: 9780792356653
• ISBN10: 0792356659
• Format: Hardcover
• Copyright: 1999-03-01
• Publisher: Kluwer Academic Pub

Summary

This book summarizes very recent developments - both applied and theoretical - in nonlinear and nonsmooth mathematics. The topics range from the highly theoretical (e.g. infinitesimal nonsmooth calculus) to the very applied (e.g. stabilization techniques in control systems, stochastic control, nonlinear feedback design, nonsmooth optimization). The contributions, all of which are written by renowned practitioners in the area, are lucid and self contained. Audience: First-year graduates and workers in allied fields who require an introduction to nonlinear theory, especially those working on control theory and optimization.

Table of Contents

Preface	vii
Key to group picture	xi
Participants	xiii
Contributors	xx
Viscosity solutions and analysis in L∞	1	(60)
E. N. Barron
Multifunctional and functional analytic techniques in nonsmooth analysis	61	(98)
Jonathan M. Browein
Qiji J. Zhu
Relaxes optimal control problems and applications to shape optimization	159	(48)
Guiseppe Buttazzo
Invariance, monotonicity, and applications	207	(100)
F. H. Clarke
Yu. S. Ledyaev
R. J. Stern
On the stabilization of some nonlinear control systems: results, tools, and applications	307	(62)
Jean-Michel Coron
Smooth variational principles and non-smooth analysis in Banach spaces	369	(38)
Robert Deville
Controlled Markov processes and mathematical finance	407	(40)
Wendell H. Eleming
Variational methods in local and global non-smooth analysis	447	(56)
Alexander Ioffe
BSDEs, weak convergence and homogenization of semilinear PDEs	503	(48)
Etienne Pardoux
Stability and stabilization: discontinuities and the effect of disturbances	551	(48)
Eduardo D. Sontag
Index	599