Optimal control and forecasting of complex dynamical systems
Chaotic behavior in systems Control theory Differentiable dynamical systems Mathematical optimization e-böcker
World Scientific
2006
EISBN 9789812774248
Cover.
Preface.
TOC$Contents.
CH$Chapter 1. Analytical methods in control and optimization.
1.1 Calculus of variations.
1.1.1 The beginning: Fermat's variational principle.
1.1.2 The "beautiful" Brachistochrone Problem.
1.1.3 Euler-Lagrange equation.
1.1.4 A word about distance between two functions.
1.1.5 The Brachistochrone problem revisited.
1.1.6 Generalizations of the Euler-Lagrange equation.
1.1.7 Transversality conditions.
1.1.8 Conditional extremum: Lagrange multipliers method.
1.1.9 Mixed Optimal problem.
1.1.10 Approximate methods of solution-Ritz's method.
1.2 Optimal control theory.
1.2.1 Sensitivity analysis.
1.2.2 Null controllability.
1.2.3 Problems with constrained control.
1.3 Summary.
CH$Chapter 2. Numerical optimization.
2.1 The halting problem and No Free Lunch Theorem &
The core of classical economic analysis represented by William Petty and Adam Smith concentrated on the field of development economics. This classical footing of the study of development is different from the neoclassical perspective in two important respects: it focuses on division of labor as the driving force of development, and it emphasizes the role of the market (the "invisible hand") in exploiting productivity gains that are derived from division of labor. However these aspects have received little attention in the body of literature that represents the modern field of development economics - which largely represents the neoclassical application of marginalism. A notable exception is research that utilizes inframarginal analysis of individuals' networking decisions in an attempt to formalize the classical mechanisms that drive division of labor. This book is a first attempt to collect relevant key contributions and is intended for active researchers in the field of development economics.
Preface.
TOC$Contents.
CH$Chapter 1. Analytical methods in control and optimization.
1.1 Calculus of variations.
1.1.1 The beginning: Fermat's variational principle.
1.1.2 The "beautiful" Brachistochrone Problem.
1.1.3 Euler-Lagrange equation.
1.1.4 A word about distance between two functions.
1.1.5 The Brachistochrone problem revisited.
1.1.6 Generalizations of the Euler-Lagrange equation.
1.1.7 Transversality conditions.
1.1.8 Conditional extremum: Lagrange multipliers method.
1.1.9 Mixed Optimal problem.
1.1.10 Approximate methods of solution-Ritz's method.
1.2 Optimal control theory.
1.2.1 Sensitivity analysis.
1.2.2 Null controllability.
1.2.3 Problems with constrained control.
1.3 Summary.
CH$Chapter 2. Numerical optimization.
2.1 The halting problem and No Free Lunch Theorem &
The core of classical economic analysis represented by William Petty and Adam Smith concentrated on the field of development economics. This classical footing of the study of development is different from the neoclassical perspective in two important respects: it focuses on division of labor as the driving force of development, and it emphasizes the role of the market (the "invisible hand") in exploiting productivity gains that are derived from division of labor. However these aspects have received little attention in the body of literature that represents the modern field of development economics - which largely represents the neoclassical application of marginalism. A notable exception is research that utilizes inframarginal analysis of individuals' networking decisions in an attempt to formalize the classical mechanisms that drive division of labor. This book is a first attempt to collect relevant key contributions and is intended for active researchers in the field of development economics.
