Vector-valued optimization problems in control theory, Volume 148 (Mathematics in Science and Engineering)

✍ Scribed by Casti (editor)

• Publisher: Academic Press
• Year: 1979
• Tongue: English
• Leaves: 231
• Category: Library

✦ Synopsis

Text: English, Russian (translation)

✦ Table of Contents

Front Cover
Vector-Valued Optimization Problems in Control Theory
Copyright Page
Contents
Introduction
Chapter 1. A Survey of Optimization Problems with Vector Criteria
1.1 General Survey of the Problem
1.2 The Remarks of L. A. Zadeh
1.3 Optimization of an Ordered Set of Scalar Criteria
1.4 Hierarchical Ranking of Scalar Criteria
1.5 Unimprovable Solutions in the Problem of Vector Optimization (Pareto Optimality)
1.6 The Work of A. Salamma and V. Gourishankar
1.7 Solutions in Fuzzy Neighborhoods
Chapter 2. The Formulation of Optimization Problems with Vector Functionals
2.1 The General Mathematical Formulation of the Problem
2.2 A Statement of Optimal Trajectory Programming Problems with a Vector–Valued Criterion
2.3 Flight at a Prescribed Altitude
2.4 Analytic Construction of Optimal Regulators
Chapter 3. The Existence of Solutions in Optimization Problems with Vector–Valued Criteria
3.1 Formulation of the Existence Problem
3.2 The Maximum Principle for the Problem of Mayer with a Scalar Functional
3.3 The Maximum Principle for Vector Optimization Problems
3.4 The Flight of a Pilotless Aircraft
3.5 On Sufficient Conditions for Problems of Scalar Optimization
3.6 On Sufficient Conditions for Problems of Vector Optimization
Chapter 4. Programming Optimal Trajectories for Problems with Vector–Valued Criteria
4.1 Introduction
4.2 A General Approach to the Solution of Programming Problems
4.3 A Simple Second-Order Example
4.4 On the Problem of Optimal Flight to a Given Location
4.5 Vertical Flight of a Rocket in a Vacuum
Chapter 5. A. Letov's Problem. The Analytic Construction of Optimal Regulators for Problems with Vector–Valued Criteria
5.1 The Problem of Analytic Construction
5.2 The Solution of the General ACOR Problem for Vector Functionals by Dynamic Programming
5.3 An Example
5.4 Vector Functionals in Linear ACOR Problems
5.5 An Example
Chapter 6. The Optimization of Vector Functionals in Linear (Nonlinear) Programming Problems
6.1 The Linear Programming Problem
6.2 The General Programming Problem
6.3 A More General Problem
6.4 Ordered Sets in Programming Problems
6.5 A Different Statement of the Linear (Nonlinear) Programming Problem for Vector Criteria
6.6 Determination of the Vector-Optimal Plan
6.7 Compromise Solutions
6.8 The Existence of a Vector-Optimal Plan
6.9 A Numerical Example of the Determination of a Vector-Optimal Plan
6.10 A Planning Problem in the Metallurgical Industry
Chapter 7. Parameter Optimization in Engineering Systems
7.1 Problem Statement
7.2 The Problem of Parameter Optimization for Heat Exchange in a Nuclear Power Station
7.3 The Parameter Optimization Problem for the Condenser of the BRGD-1000
7.4 A Search Algorithm
Bibliography