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Complexity and control : towards a rigorous behavioral theory of complex dynamical systems /
The book Complexity and Control: Towards a Rigorous Behavioral Theory of Complex Dynamical Systems is a graduate-level monographic textbook, intended to be a novel and rigorous contribution to modern Complexity Theory. This book contains 11 chapters and is designed as a one-semester course for engin...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
[2015]
|
| Colección: | Series on stability, vibration, and control of systems.
volume 20. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Contents
- Preface
- Acknowledgments
- Glossary of Frequently Used Symbols
- 1 Introduction
- 2 Local Geometrical Machinery for Complexity and Control
- 2.1 Introduction: Why Kahler Manifolds?
- 2.1.1 Dynamical Prologue: Complex Hamiltonian Dynamics
- 2.1.2 Unified Behavioral Picture: Kahler Geometrodynamics
- 2.2 Complex Manifolds and Their Vector Bundles
- 2.2.1 Behavioral Dynamics on Complex Plane
- Behavioral dynamics in the complex plane C
- Holomorphic functions and their differential operators in C
- Residues of meromorphic functions in C
- 2.2.2 3D Rotations: Spinors2.2.3 Attractor Dynamics on Riemann Surfaces
- Why Riemann surfaces?
- 2.2.4 Complex Manifolds and Vector Bundles
- 2.2.5 (Co)Tangent Spaces to the Complex Manifold
- 2.2.6 Complex Vector Bundles
- 2.3 From Kalman Systems to Riemann Manifolds
- 2.4 Basic Kahler Geometry
- 2.4.1 Essential Kahler Tensors and Cohomology Groups
- 2.4.2 Global Kahler Geometry
- Fano manifolds
- Kahler structures
- Two Kahler structures and two alternative points of view
- 2.4.3 Local Kahler Geometry
- Symplectic coordinates
- 2.4.4 Invariant Hamiltonian Dynamics on Kahler Manifolds2.5 Dynamics on Quaternion-Kahler Manifolds
- 2.5.1 Quaternion-Kahler Manifolds
- 2.5.2 Hamiltonian Dynamics on Quaternion-Kahler Manifolds
- 2.5.3 Lagrangian Dynamics on Quaternion-Kahler Manifolds
- 2.6 Kahler-Ricci-Flow Framework
- 2.6.1 Motivation for the Kahler-Ricci Flow
- 2.6.2 Ricci Flow on a Kahler Manifold
- 2.6.3 Definition of the Kahler-Ricci Flow
- 2.6.4 Evolution of the Kahler-Perelman Entropy
- 2.7 Summary of Kahler-Ricci Geometrical Dynamics
- 2.8 Appendix
- ""2.8.1 Real Banach and Complex Hilbert Spaces""""2.8.2 From Linear to Nonlinear MIMO Control Theory""; ""Kalman�s Linear State-Space Formalism""; ""Basics of Kalman Filtering""; ""Extended (Nonlinear) Kalman Filter""; ""Ensemble Kalman Filter and Nonlinear Estimation""; ""Affine Nonlinear Control System""; ""Lie Derivative and Lie Bracket in Control Theory""; ""Example: Car-Parking Using Lie Brackets""; ""2.8.3 Basic Complexity Geometrodynamics""; ""Basic Tensor Machinery""; ""Tensor Derivatives on Riemannian Manifolds""; ""Covariant Form of Gradient, Divergence, Curl and Laplacian""
- ""The Absolute Derivative and 3D Curve Geometry""""Covariant state equation""; ""Basic Exterior Machinery""; ""Basic Manifold Machinery""; ""Tensor Fields and Bundles""; ""Basic de Rham Machinery""; ""Exterior Lagrangian Systems""; ""Basic Gauge Fields""; ""Basic Lie Groups and Their Lie Algebras""; ""2.8.4 Advanced Complexity Geometrodynamics""; ""Basic Riemannian-Ricci Machinery""; ""Basic Hamiltonian Machinery""; ""Pontryagin�s Maximum Principle""; ""Affine Control Systems""; ""Basic Hodge Machinery""; ""Basic Applications to Quantum Field Theory""; ""Lie Algebra-Valued Exterior Forms""