Complexity and control : towards a rigorous behavioral theory of complex dynamical systems

• Main Authors: Ivancevic, Vladimir G. (Author), Reid, Darryn J. (Author)
• Format: Electronic eBook
• Language: English
• Published: New Jersey : World Scientific, [2015]
• Series: Series on stability, vibration, and control of systems. volume 20.
• Subjects: Differentiable dynamical systems.; Chaotic behavior in systems.; System analysis.; Control theory.; Computational complexity.; elektronické knihy; electronic books
• ISBN: 9789814635875; 9814635871; 9781680158502; 1680158503; 9789814635868; 9814635863
• Physical Description: 1 online resource (xix, 589 pages)

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...

Table of Contents:

• 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""; ""Kalmanâ€?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""; ""Pontryaginâ€?s Maximum Principle""; ""Affine Control Systems""; ""Basic Hodge Machinery""; ""Basic Applications to Quantum Field Theory""; ""Lie Algebra-Valued Exterior Forms""