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Contemporary trends in nonlinear geometric control theory and its applications /
Annotation 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....
| Clasificación: | Libro Electrónico |
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| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
River Edge, NJ :
World Scientific,
©2002.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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 Survey1. 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 approach6. 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 systems3. 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 Systems1. 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.