Advances in nonlinear dynamics and control

The mathematical community of the former Soviet Union has long been known for its work on nonlinear dynamics, particularly as applied to uncertain systems in a deterministic setting. This book presents a coherent collection of overviews of some of that research, concentrating on the three main branches of uncertain dynamics - differential games; evolution; estimation and control; and robust stabilization. The application of these techniques to nonlinear systems as well as the global optimization of the latter are also among the issues treated in the volume. The techniques range from those common in engineering control communities to those that are more purely mathematical in nature. Extended bibliographies for each contribution will be invaluable in bringing to the attention of Western research workers a considerable number of publications hitherto unknown to them. Research workers and graduate students in nonlinear systems and control will find here a wealth of new ideas and techniques, as well as a self-contained introduction to an important body of mathematical literature. Series: Progress in Systems and Control Theory, Volume 17 (PSCT) Contents: Preface/C. Byrnes Editor's Remarks The Decomposition of Controlled Dynamic Systems/F.L. Chernousko A Differential Game for the Minimax of a Positional Functional/N.N. Krasovskii, A.N. Krasovskii Global Methods in Optimal Control Theory/V.F. Krotov On the Theory of Trajectory Tubes - a Mathematical Formalism for Uncertain Dynamics, Viability and Control/A.B. Kurzhanski, T.F. Filippova A Theory of Generalized Solutions to First-Order PDEs with an Emphasis on Differential games/A.I. Subbotin Adaptivity and Robustness in Automatic Control Systems/Ya. Z. Tsypkin