Iterative Dynamic Programming

Iterative Dynamic Programming

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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 more

Product details

  • Hardback | 344 pages
  • 163.1 x 241.3 x 23.6mm | 711.64g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 2003.
  • 57 black & white tables
  • 1584881488
  • 9781584881483

Review quote

"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, 2001show more

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 more