Complexity and control : towards a rigorous behavioral theory of complex dynamical systems / Vladimir G Ivancevic (Defence Science & Technology Organisation, Australia), Darryn J Reid (Defence Science & Technology Organisation, Australia).

Format:

Book

Author/Creator:

Ivancevic, Vladimir G., author.

Reid, Darryn J., author.

Series:

Series on stability, vibration, and control of systems. Series A ; v. 20.

Series on stability, vibration and control of systems, Series A Complexity and control

Language:

English

Subjects (All):

Differentiable dynamical systems.

Chaotic behavior in systems.

System analysis.

Control theory.

Computational complexity.

Physical Description:

1 online resource (610 p.)

Place of Publication:

Singapore ; Hackensack, New Jersey : World Scientific Publishing Company, 2015.

Language Note:

English

Summary:

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 engineers; applied and pure mathematicians; theoretical and experimental physicists; computer and economic scientists; theoretical chemists and biologists, as well as all mathematically educated scientists and students, both in industry and academia, interested in predicting and controlling complex dynamical systems of arbitrary nature.

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: Spinors

2.2.3 Attractor Dynamics on Riemann SurfacesWhy 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 Manifolds; 2.5 Dynamics on Quaternion-Kahler Manifolds

2.5.1 Quaternion-Kahler Manifolds2.5.2 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 FilterEnsemble 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 FieldsBasic 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; Exterior Connection, Curvature and Torsion; Cartan Calculus; Cartan Equations, Gauge Potential and Field Strength; 3 Global Categorical Framework for Complexity and Control; 3.1 Introduction; 3.2 Categories, Functors and Naturality; 3.2.1 Categories; 3.2.2 Functors

3.2.3 Natural Transformations

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-68015-850-3

981-4635-87-1

OCLC:

922951968