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Discrete-time optimal control problems with general constraints

Editor: Robert J. Renka Authors:

M. E. Fisher,

L. S. JenningsAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 18, Issue 4

Pages 401 - 413

https://doi.org/10.1145/138351.138356

Published: 01 December 1992 Publication History

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Abstract

This paper presents a computational procedure for solving combined discrete-time optimal control and optimal parameter selection problems subject to general constraints. The approach adopted is to convert the problem into a nonlinear programming problem which can be solved using standard optimization software. The main features of the procedure are the way the controls are parametrized and the conversion of all constraints into a standard form suitable for computation. The software is available commercially as a FORTRAN program DMISER3 together with a companion program MISER3 for solving continuous-time problems.

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Teo KLi BYu CRehbock VTeo KLi BYu CRehbock V(2021)Discrete Time Optimal Control ProblemsApplied and Computational Optimal Control10.1007/978-3-030-69913-0_5(121-172)Online publication date: 19-Feb-2021
https://doi.org/10.1007/978-3-030-69913-0_5
Barro DCanestrelli E(2016)Combining stochastic programming and optimal control to decompose multistage stochastic optimization problemsOR Spectrum10.1007/s00291-015-0427-638:3(711-742)Online publication date: 1-Jul-2016
https://dl.acm.org/doi/10.1007/s00291-015-0427-6
Tran VBrdys M(2010)Robustly Feasible Optimizing Control of Network Systems under Uncertainty and Application to Drinking Water Distribution SystemsIFAC Proceedings Volumes10.3182/20100712-3-FR-2020.0005143:8(304-309)Online publication date: 2010
https://doi.org/10.3182/20100712-3-FR-2020.00051
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Index Terms

Discrete-time optimal control problems with general constraints
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
    2. Numerical analysis
      1. Numerical differentiation
  2. Mathematical software
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization

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Reviews

Reviewer: Andrew Donald Booth

The computational procedures required to digitally solve optimal control problems with constraints are described. A brief introduction discusses existing methods and gives appropriate references. This leads quickly to a description of the DMISER3 program produced by the authors. Neither the program description nor the brief discussion of the analytical underpinning is adequate to allow an evaluation of the method, which appears to need user input not only of the relevant analytical functions but also of their first partial derivatives. As far as I can gather, the procedures resemble those in the Levenberg-Marquand nonlinear optimization method. An example application is discussed: the buckled beam with internal loading. The running times on a SUN SPARCstation and the associated outputs that are tabulated seem at least competitive with existing methods. Any real evaluation would require access to the software, which is said to be commercially available. An adequate set of references is provided.

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Information

Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 18, Issue 4

Dec. 1992

117 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/138351

Editor:
Robert J. Renka
Univ. of North Texas, Denton

Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 December 1992

Published in TOMS Volume 18, Issue 4

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https://doi.org/10.1007/978-3-030-69913-0_5
Barro DCanestrelli E(2016)Combining stochastic programming and optimal control to decompose multistage stochastic optimization problemsOR Spectrum10.1007/s00291-015-0427-638:3(711-742)Online publication date: 1-Jul-2016
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Tran VBrdys M(2010)Robustly Feasible Optimizing Control of Network Systems under Uncertainty and Application to Drinking Water Distribution SystemsIFAC Proceedings Volumes10.3182/20100712-3-FR-2020.0005143:8(304-309)Online publication date: 2010
https://doi.org/10.3182/20100712-3-FR-2020.00051
Kormann KHolmgren SKarlsson H(2010)A Fourier-Coefficient Based Solution of an Optimal Control Problem in Quantum ChemistryJournal of Optimization Theory and Applications10.1007/s10957-010-9735-9147:3(491-506)Online publication date: 21-Jul-2010
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Wong KJennings L(1996)Long term planning of hydro-thermal power systemsWorld Congress of Nonlinear Analysts '9210.1515/9783110883237.2723Online publication date: 31-Jan-1996
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Rehbock VTeo KJennings LLee C(1992)An exact penalty function approach to all-time-step constrained discrete-time optimal control problemsApplied Mathematics and Computation10.1016/0096-3003(92)90025-V49:2-3(215-230)Online publication date: 1-Jun-1992
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Abstract

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Index Terms

Recommendations

Sampled-Data and Discrete-Time $H_2$ Optimal Control

Robustly Exponential Stability Analysis for Discrete-Time Stochastic Neural Networks with Interval Time-Varying Delays

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