Nonlinear analysis, differential equations and control : [proceedings of the NATO Advanced Study Institute and Séminarie de Mathématiques Supérieures on Nonlinear Analysis, Differential Equations and Control, Montréal, Canada, July 27 - August 7, 1998

Recent years have witnessed important developments in those areas of the mathematical sciences where the basic model under study is a dynamical system such as a differential equation or control process. Many of these recent advances were made possible by parallel developments in nonlinear and nonsmooth analysis. The latter subjects, in general terms, encompass differential analysis and optimization theory in the absence of traditional linearity, convexity or smoothness assumptions. In the last three decades it has become increasingly recognized that nonlinear and nonsmooth behavior is naturally present and prevalent in dynamical models, and is therefore significant theoretically. This point of view has guided us in the organizational aspects of this ASI. Our goals were twofold: We intended to achieve "cross fertilization" between mathematicians who were working in a diverse range of problem areas, but who all shared an interest in nonlinear and nonsmooth analysis. More importantly, it was our goal to expose a young international audience (mainly graduate students and recent Ph. D. 's) to these important subjects. In that regard, there were heavy pedagogical demands placed upon the twelve speakers of the ASI, in meeting the needs of such a gathering. The talks, while exposing current areas of research activity, were required to be as introductory and comprehensive as possible. It is our belief that these goals were achieved, and that these proceedings bear this out. Each of the twelve speakers presented a mini-course of four or five hours duration. Front Matter....Pages i-xix Viscosity solutions and analysis in L ∞....Pages 1-60 Multifunctional and functional analytic techniques in nonsmooth analysis....Pages 61-157 Relaxed optimal control problems and applications to shape optimization....Pages 159-206 Invariance, monotonicity, and applications....Pages 207-305 On the stabilization of some nonlinear control systems: results, tools, and applications....Pages 307-367 Smooth variational principles and non-smooth analysis in Banach spaces....Pages 369-405 Controlled Markov processes and mathematical finance....Pages 407-446 Variational methods in local and global non-smooth analysis....Pages 447-502 BSDEs, weak convergence and homogenization of semilinear PDEs....Pages 503-549 Stability and stabilization: discontinuities and the effect of disturbances....Pages 551-598 Back Matter....Pages 599-602

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, shastic 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.

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. Proceedings of the NATO Advanced Study Institute, Université de Montréal, Canada, July 27-August 7, 1998 Proceedings of the NATO Advanced Study Institute, Universite de Montreal, Canada, July 27-August 7, 1998