Contemporary Trends in Nonlinear Geometric Control Theory and Its Applications.
Title:
Contemporary Trends in Nonlinear Geometric Control Theory and Its Applications.
Author:
Anzaldo-Meneses, A.
ISBN:
9789812778079
Personal Author:
Physical Description:
1 online resource (495 pages)
Contents:
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 curves -- Controllability 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 case -- 7. 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 one -- 5. 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. Introduction -- 2. 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 connection -- 7. Five modern variations on the theme of the brachistochrone -- Part II Contributed Chapters -- Symplectic Methods for Strong Local Optimality in the Bang-bang Case -- 1. Introduction -- 2. Main results -- 3. Sketch of the proof -- Charges in Magnetic Fields and Sub-Riemannian Geodesics -- 1. Introduction -- 2. Sub-Riemannian geometry and classical particles -- 3. Polynomial magnetic fields -- 4. Linear magnetic fields and Cartan's five dimensional case.
Topological Versus Smooth Linearization of Control Systems -- 1. Introduction -- 2. Preliminaries on equivalence of control systems -- 3. Main result on topological linearization -- 4. An open question -- 5. Implications in control theory -- Local Approximation of the Reachable Set of Control Processes -- 1. Introduction -- 2. Tangent cones -- 3. Examples of g-variations -- 4. Applications -- 5. Open problems -- Geometric Optimal Control of the Atmospheric Arc for a Space Shuttle -- 1. Introduction -- 2. The model -- 3. The control problem -- 4. The minimal principle without state constraints-extremal curves -- 5. Optimal control with state constraints -- High-Gain and Non-High-Gain Observers for Nonlinear Systems -- 1. Introduction systems under consideration -- 2. Justification of the assumptions and observability -- 3. Statement and proof of the theoretical result -- 4. Application: observation of a binary distillation column -- 5. Appendix: Technical lemmas -- Lie Systems in Control Theory -- 1. Introduction -- 2. Systems of differential equations admitting a superposition rule -- 3. Control and controllability of systems on Lie groups -- 4. The Wei-Norman method -- 5. Illustrative examples -- From the Geometry to the Algebra of Nonlinear Observability -- 1. Introduction -- 2. The differential algebraic geometric approach -- 3. Computing -- Appendix: Basic differential algebraic geometry -- Appendix: Characteristic sets -- Existence Theorems in Nonlinear Realization Theory and a Cauchy-Kowalewski Type Theorem -- 1. Introduction -- 2. Existence of analytic realizations -- 3. Convergence along vector fields and their commutators -- 4. Existence of analytic solutions of PDE's -- Normality Local Controllability and NOC for Multiobjective Optimal Control Problems -- 1. Introduction -- 2. Background.
3. Normality implies seminormality -- 4. Hamiltonian normality implies seminormality -- 5. Normality implies seminormality for systems of Mayer type -- 6. NOC for multiobjective optimal control problems -- Controllability and Coordinates of the First Kind -- 1. Introduction -- 2. Integral manifolds and controllability -- 3. Separating invariant flows from time-varying functionals -- 4. Coordinates of the 1st kind -- 5. Supporting hyperplanes -- Variational Equations of Lagrangian Systems and Hamilton's Principle -- 1. Introduction -- 2. The variational pinciple -- 3. Symmetries and constants of motion -- 4. Intrinsic formulation -- 5. Examples -- Control of the Hovercraft Vessel: A Flatness plus Second Order Sliding Mode Control Approach -- 1. Introduction -- 2. The hovercraft model -- 3. Trajectory tracking for the hovercraft system -- 4. Simulation results -- Optimality of Singular Trajectories and Asymptotics of Accessibility Sets under Generic Assumptions -- 1. Introduction -- 2. Optimality of singular trajectories -- 3. Asymptotics of the accessibility sets -- Control Theory and Holomorphic Diffeomorphisms -- 1. Introduction -- 2. Complex analytic considerations -- 3. Holomorphic vector fields -- 4. Jets -- Index.
Abstract:
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 articles specially written by colleagues and friends of Vel Jurdjevic, all of them leading applied mathematicians and control theorists. There is also place for surveys on topics of current research which present the state of the art of modern geometric control theory. Finally, the volume contains several new mathematical ideas generated by geometric control theory techniques, which may initiate new directions of research beyond control theory. Contents: Invited Survey Chapters: Variational Problems on Lie Groups and Their Homogeneous Spaces: Elastic Curves, Tops, and Constrained Geodesic Problems (V Jurdjevic & F Monroy-Pérez); Controllability of Lie Systems (J D Lawson & D Mittenhuber); Canonical Contact Systems for Curves: A Survey (W Respondek & W Pasillas-Lépine); The Brachistochrone Problem and Modern Control Theory (H J Sussmann & J C Willems); Contributed Chapters: Symplectic Methods for Strong Local Optimality in the Bang-Bang Case (A Agrachev et al.); Charges in Magnetic Fields and Sub-Riemannian Geodesics (A A Anzaldo-Meneses & F Monroy-Pérez); Topological Versus Smooth Linearization of Control Systems (L Baratchart et al.); Local Approximation of the Reachable Set of Control Processes (R M Bianchini); Geometric Optimal Control of the Atmospheric Arc
for a Space Shuttle (B Bonnard et al.); High-Gain and Non-High-Gain Observers for Nonlinear Systems (E Busvelle & J P Gauthier); Lie Systems in Control Theory (J F Cariñena & A Ramos); From the Geometry to the Algebra of Nonlinear Observability (S Diop); Existence Theorems in Nonlinear Realization Theory and a Cauchy-Kowalewski Type Theorem (B Jakubczyk); Normality, Local Controllability and NOC for Multiobjective Optimal Control Problems (A Jourani); and Coordinates of the First Kind (M Kawski); Variational Equations of Lagrangian Systems and Hamilton's Principle (H N Núñez-Yépez et al.); Control of the Hovercraft Vessel: A Flatness Plus Second Order Sliding Mode Control Approach (H Sira-Ramírez); Optimality of Singular Trajectories and Asymptotics of Accessibility Sets Under Generic Assumptions (E Trélat); Control Theory and Holomorphic Diffeomorphisms (D Varolin). Readership: Control theorists, control engineers and chemical engineers.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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