Iterative Dynamic Programming: 1st Edition (Hardback) book cover

Iterative Dynamic Programming

1st Edition

By Rein Luus

Chapman and Hall/CRC

344 pages

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Hardback: 9781584881483
pub: 2000-01-27
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Description

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 scheme have made the computational procedure feasible.

With iteration, dynamic programming becomes an effective optimization procedure for very high-dimensional optimal control problems and has demonstrated applicability to singular control problems. Recently, iterative dynamic programming (IDP) has been refined to handle inequality state constraints and noncontinuous functions.

Iterative Dynamic Programming offers a comprehensive presentation of this powerful tool. It brings together the results of work carried out by the author and others - previously available only in scattered journal articles - along with the insight that led to its development. The author provides the necessary background, examines the effects of the parameters involved, and clearly illustrates IDP's advantages.

Reviews

"This book provides a working knowledge of IDP with many worked out solutions for a wide range of problems. This is especially useful for graduate students and industrial practitioners because a strong background in mathematical techniques and chemical engineering is not essential for understanding this book. This book can be used in a university as a textbook at the level of seniors or first-year graduate students. Of course, this book is also suitable for academic researchers who need an alternative way to cross-validate their solutions to OCPs with their newly devised methods… It can be concluded that this text is a very good addition to the toolbox for numerical optimal control. It is expected that all engineers, graduate students, researchers who are involved in solving optimal control problems should know IDP - the new powerful OCP solution scheme."

-International Journal of Robust and Nonlinear Control, vol. 11, no. 14, December 15, 2001

Table of Contents

INTRODUCTION

Fundamental Definitions and Notation

Steady-State System Model

Continuous-Time System Model

Discrete-Time System Model

The Performance Index

Interpretation of Results

Examples of Systems for Optimal Control

Solving Algebraic Equations

Solving Ordinary Differential Equations

STEADY-STATE OPTIMIZATION

Linear Programming

LJ Optimization Procedure

References

DYNAMIC PROGRAMMING

Introduction

Examples

Limitations of Dynamic Programming

ITERATIVE DYNAMIC PROGRAMMING

Construction of Time Stages

Construction of Grid for x

Allowable Values for Control

First Iteration

Iterations with Systematic Reduction in Region Size

Example

Use of Accessible States as Grid Points

Algorithm for IDP

Early Applications of IDP

ALLOWABLE VALUES FOR CONTROL

Introduction

Comparison of Uniform Distribution to Random Choice

EVALUATION OF PARAMETERS IN IDP

Number of Grid Points

Multi-Pass Approach

Further Example

PIECEWISE LINEAR CONTINUOUS CONTROL

Problem Formulation

Algorithm for IDP for Piecewise Linear Control

Numerical Examples

TIME-DELAY SYSTEMS

Problem Formulation

Examples

VARIABLE STAGE LENGTHS

Variable Stage-Lengths when Final Time is Free

Problems where Final Time f is not Specified

Systems with Specified Final Time

SINGULAR CONTROL PROBLEMS

Four Simple-Looking Examples

Yeo's Singular Control Problem

Nonlinear Two-Stage CSTR Problem

STATE CONSTRAINTS

Introduction

Final State Constraints

State Inequality Constraints

TIME OPTIMAL CONTROL

Introduction

Time Optimal Control Problem

Direct Approach to Time Optimal Control

Examples

High Dimensional Systems

NONSEPARABLE PROBLEMS

Problem Formulation

Examples

References

SENSITIVITY CONSIDERATIONS

Introduction

Example: Lee-Ramirez Bioreactor

TOWARD PRACTICAL OPTIMAL CONTROL

Optimal Control of Oil Shale Pyrolysis

Future Directions

APPENDICES: Nonlinear Algebraic Equation Solver. Listing of Linear Programming Program. LJ Optimization Programs. Iterative Dynamic Programming Programs. Listing of DVERK.

INDEX

Each chapter also contains an introduction and a References section.

About the Series

Monographs and Surveys in Pure and Applied Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied