Iterative Dynamic Programming

Rein Luus

• Publisher: Chapman and Hall/CRC
• Year: 2019
• ISBN:
  9780429525094
• Edition: 1
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Dynamic programming is a powerful method for solving optimization problems, but has a number of drawbacks that limit its use to solving problems of very low dimension. To overcome these limitations, author Rein Luus suggested using it in an iterative fashion. Although this method required vast computer resources, modifications to his original schem

Chapter 1

Fundamental concepts

1.1 Introduction

Optimization, or optimal control, in the sense to be used in this book, is concerned with determining the largest value or the smallest value for some criterion of performance. For example, if we are dealing with economic benefit, then we would like to choose the conditions for operating the system so that the economic benefit would be maximized. If, however, the criterion of performance is chosen to be the cost, then the system should be operated to minimize the cost. In each case we seek the operating conditions that yield the extreme value for the performance criterion.

It is obvious that the operating procedure is dictated by the choice of the criterion of operation. The choice of such criterion is not straightforward, since there are numerous factors that must be taken into consideration, such as productivity, profit, cost, environmental impact, reliability, yield of a reactor, quality of product, etc. We may want to have more than one criterion for optimization. For the present work, however, we assume that all the objectives can be expressed in terms of an appropriate scalar criterion of performance which we call performance index, with the understanding that the optimization results will be dependent on such a choice. It is also important to express this performance index in terms of the same variables that are used in the mathematical model of the physical system or process under consideration.

For the development of the mathematical model of the system, we need some insight into the behavior of the physical system, and how the variables at our disposal may be used to change its behavior. Such a relationship may be expressed in terms of algebraic equations, ordinary differential equations, difference equations, partial differential equations, integral equations, or combinations of them. The simplest situation arises, of course, if the model is described in terms of ...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Dedication
• About the author
• Preface
• Notation
• Table of Contents
• 1 Fundamental concepts
• 2 Steady-state optimization
• 3 Dynamic programming
• 4 Iterative dynamic programming
• 5 Allowable values for control
• 6 Evaluation of parameters in IDP
• 7 Piecewise linear control
• 8 Time-delay systems
• 9 Variable stage lengths
• 10 Singular control problems
• 11 State constraints
• 12 Time optimal control
• 13 Nonseparable problems
• 14 Sensitivity considerations
• 15 Toward practical optimal control
• A Nonlinear algebraic equation solver
• B Listing of linear programming program
• C LJ optimization programs
• D Iterative dynamic programming programs
• E Listing of DVERK
• Index