Control and nonlinearity

This book presents methods to study the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions. The emphasis is put on specific phenomena due to nonlinearities. In particular, many examples are given where nonlinearities turn out to be essential to get controllability or stabilization. Various methods are presented to study the controllability or to construct stabilizing feedback laws. The power of these methods is illustrated by numerous examples coming from such areas as celestial mechanics, fluid mechanics, and quantum mechanics. The book is addressed to graduate students in mathematics or control theory, and to mathematicians or engineers with an interest in nonlinear control systems governed by ordinary or partial differential equations. Preface -- Finite-dimensional Linear Control Systems -- Linear Partial Differential Equations -- Controllability Of Nonlinear Systems In Finite Dimension -- Linearized Control Systems And Fixed-point Methods -- Iterated Lie Brackets -- Return Method -- Quasi-static Deformations -- Power Series Expansion -- Previous Methods Applied To A Schrödinger Equation -- Linear Control Systems In Finite Dimension And Applications To Nonlinear Control Systems -- Stabilization Of Nonlinear Control Systems In Finite Dimension -- Feedback Design Tools -- Applications To Some Partial Differential Equations -- Appendix A. Elementary Results On Semigroups Of Linear Operators -- Appendix B. Degree Theory. Jean-michel Coron. Includes Bibliographical References (p. 397-420) And Index.