04976nam 22006374a 450 991078498480332120230607221557.0981-277-807-1(CKB)1000000000408471(EBL)1681534(OCoLC)879074416(SSID)ssj0000129793(PQKBManifestationID)11139114(PQKBTitleCode)TC0000129793(PQKBWorkID)10078942(PQKB)11601836(MiAaPQ)EBC1681534(WSP)00004879(Au-PeEL)EBL1681534(CaPaEBR)ebr10201240(CaONFJC)MIL505434(EXLCZ)99100000000040847120020514d2002 uy 0engur|n|---|||||txtccrContemporary trends in nonlinear geometric control theory and its applications[electronic resource] /A. Anzaldo-Meneses ... [et al.]River Edge, NJ World Scientificc20021 online resource (496 p.)Description based upon print version of record.981-02-4841-5 Includes bibliographical references and index.Contents ; Foreword ; Part I Invited Survey Chapters ; Variational Problems on Lie Groups and their Homogeneous Spaces: Elastic Curves Tops and Constrained Geodesic Problems ; 1. Introduction ; 2. Space forms and their frame bundles ; 3. Hamiltonians and the extremal curvesControllability of Lie Systems 1. Introduction ; 2. Control systems on Lie groups ; 3. Groups irrelevant for transitivity ; 4. Exploiting compactness and irrelevancy ; 5. Irrelevant groups and algebras ; 6. Irrelevant groups and algebras: the solvable case7. Irrelevant groups and algebras: the semisimple case Canonical Contact Systems for Curves: A Survey ; 1. Introduction ; 2. The canonical contact system for curves ; 3. History ; 4. Involutive subdistributions of corank one5. Contact systems characteristic distributions and involutive subdistributions 6. Flatness of contact systems ; 7. An example ; 8. Singular points and extended Kumpera-Ruiz normal forms ; The Brachistochrone Problem and Modern Control Theory ; 1. Introduction2. Johann Bernoulli and the brachistochrone problem 3. The standard formulation and Johann Bernoulli's solution ; 4. Spurious solutions and the calculus of variations approach ; 5. The optimal control approach ; 6. The differential-geometric connection7. Five modern variations on the theme of the brachistochrone Mathematical control theory has evolved from the study of practical problems in engineering and sciences to the elaboration of deep, important concepts in mathematics and applied sciences. This volume concerns contemporary trends in nonlinear geometric control theory and its applications. It is a fine collection of papers presenting new results, relevant open problems, and important applications regarding academic and real-world problems. The book is dedicated to Velimir Jurdjevic whose scientific activity has been influential in the research of many of the authors. It contains a number of aNonlinear control theoryGeometry, DifferentialExterior differential systemsNonlinear control theory.Geometry, Differential.Exterior differential systems.629.8/312Anzaldo-Meneses A1499524MiAaPQMiAaPQMiAaPQBOOK9910784984803321Contemporary trends in nonlinear geometric control theory and its applications3725623UNINA