Table of Contents
Chapter 1. Decomposition in a Singularly Perturbed System
1.1. Integral Manifolds and Separation Movements
1.2. Matrices of Integral Manifolds
1.3. Transition Matrix Singularly Perturbed System and Its Asymptotic Behavior
1.4. Converting Transition Matrix on the Integral Manifold
Chapter 2. Research Controllability and Dynamics of Movement Singularly Perturbed System
2.1. Controllability Singularly Perturbed Systems of Optimal Control with Constantly Acting External Forces
2.2. Criterion of Controllability
2.3. Estimation of The Standard Deviation of the Trajectory of the System of Movement
Chapter 3. Method of Moments in the Theory of Singularly Perturbed Systems
3.1. Statement of the Problem of How to Manage the Problem of Moments
3.2. Control with Minimal Power
Chapter 4. Research Tasks of Optimal Control of Dynamic Processes Economy
4.1. Decomposition of an Extreme Problem of Interbranch Balance
4.2. Solution of Singularly Perturbed Problem of Optimal Economic Growth
4.3. Control in Single-Commodity Macroeconomic Dynamic Model for Different Optimality Criteria
4.4. Investigation of the Problem of Optimal Control in Single-Commodity Macro Models Based on the Delay of the Process of Investments
4.5. Estimation of Optimal Development of the Economy Based on a Single-Commodity Optimization Model of with a Small Parameter
Zamirbek Imanaliev, Professor of the Department of Applied Mathematics and Informatics, Kyrgyz State Technical University after named I.Razzakov. He is engaged in problems of optimal control. He published scholarly works on the separation of variables of the optimal control problem. He mainly works on the theory of optimization and control, mathematical economics and linear programming.
Zhyrgalbubu Barakova, Head of Department of Information Systems and Technologies in telecommunications, Kyrgyz State Technical University after named I.Razzakov, PhD. She has published works on the application of optimal control to economic problems.
This book is mainly on the problem of optimal control of singularly perturbed systems and decomposition of variables. The problem of optimal control with respect to the economic processes to which the criterion of control is formulated using the Gram operator of the properties, as well as to deal with the evaluation of the standard deviation of the trajectory of motion of the system. The basic equations and formulas allows to obtain a decision applied to the method of moments, which enables unified computing optimal control of the search procedure and allows separation of variables.