附註:Includes bibliographical references (pages 443-453).
COVER -- TABLE OF CONTENTS -- GENERAL PREFACE -- PREFACE -- CHAPTER 1 OPTIMIZATION OF LINEAR SYSTEMS WITH GENERALIZED CONTROL -- 1. FORMULATION OF OPTIMIZATION PROBLEM FOR DISTRIBUTED SYSTEMS AND AUXILIARY STATEMENTS -- 2. EXISTENCE OF OPTIMAL CONTROL -- CHAPTER 2 GENERAL PRINCIPLES OF INVESTIGATION OF LINEAR SYSTEMS WITH GENERALIZED CONTROL -- 1. DIFFERENTIAL PROPERTIES OF PERFORMANCE CRITERION -- 2. REGULARIZATION OF CONTROL -- CHAPTER 3 NUMERICAL METHODS OF OPTIMIZATION OF LINEAR SYSTEMS WITH GENERALIZED CONTROL -- 1. PARAMETRIZATION OF CONTROL -- 2. PULSE OPTIMIZATION PROBLEM -- 3. ANALOGUE OF THE GRADIENT PROJECTION METHOD -- 4. ANALOGUE OF THE CONDITIONAL GRADIENT METHOD -- 5. PROBLEMS OF JOINT OPTIMIZATION AND IDENTIFICATION -- 6. GENERAL THEOREMS OF GENERALIZED OPTIMAL CONTROL -- CHAPTER 4 PARABOLIC SYSTEMS -- 1. GENERALIZED SOLVABILITY OF PARABOLIC SYSTEMS -- 2. ANALOGUE OF GALERKIN METHOD -- 3. PULSE OPTIMAL CONTROL OF PARABOLIC SYSTEMS -- CHAPTER 5 PSEUDO-PARABOLIC SYSTEMS -- 1. GENERALIZED SOLVABILITY OF PSEUDOPARABOLIC SYSTEMS (THE DIRICHLET INITIAL BOUNDARY VALUE PROBLEM) -- 2. GENERALIZED SOLVABILITY OF PSEUDOPARABOLIC SYSTEMS (THE NEUMANN INITIAL BOUNDARY VALUE PROBLEM) -- 3. PULSE OPTIMAL CONTROL OF PSEUDOPARABOLIC SYSTEMS (THE DIRICHLET INITIAL BOUNDARY VALUE PROBLEM) -- 4. PULSE OPTIMAL CONTROL OF PSEUDOPARABOLIC SYSTEMS (THE NEUMANN INITIAL BOUNDARY VALUE PROBLEM) -- CHAPTER 6 HYPERBOLIC SYSTEMS -- 1. GENERALIZED SOLVABILITY OF HYPERBOLIC SYSTEMS (THE DIRICHLET INITIAL BOUNDARY VALUE PROBLEM) -- 2. GENERALIZED SOLVABILITY OF HYPERBOLIC SYSTEMS (THE NEUMANN INITIAL BOUNDARY VALUE PROBLEM) -- 3. ANALOGIES OF GALERKIN METHOD FOR HYPERBOLIC SYSTEMS -- 4. PULSE OPTIMAL CONTROL OF HYPERBOLIC SYSTEMS (THE DIRICHLET INITIAL BOUNDARY VALUE PROBLEM) -- CHAPTER 7 PSEUDO-HYPERBOLIC SYSTEMS -- 1. GENERALIZED SOLVABILITY OF PSEUDOHYPERBOLIC SYSTEMS (THE DIRICHLET INITIAL BOUNDARY VALUE PROBLEM) -- 2. GENERALIZED SOLVABILITY OF PEUDOHYPERBOLIC SYSTEMS (THE D
摘要:The author of this book made an attempt to create the general theory of optimization of linear systems (both distributed and lumped) with a singular control. The book touches upon a wide range of issues such as solvability of boundary values problems for partial differential equations with generalized right-hand sides, the existence of optimal controls, the necessary conditions of optimality, the controllability of systems, numerical methods of approximation of generalized solutions of initial boundary value problems with generalized data, and numerical methods for approximation of optimal controls. In particular, the problems of optimization of linear systems with lumped controls (pulse, point, pointwise, mobile and so on) are investigated in detail.
