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Numerical properties of the Ritz-Trefftz algorithm for optimal control

Authors:

W. E. Bosarge, Jr.,

O. G. JohnsonAuthors Info & Claims

Communications of the ACM, Volume 14, Issue 6

Pages 402 - 406

https://doi.org/10.1145/362604.362612

Published: 01 June 1971 Publication History

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Abstract

In this paper the Ritz-Trefftz algorithm is applied to the computer solution of the state regulator problem. The algorithm represents a modification of the Ritz direct method and is designed to improve the speed of solution and the storage requirements to the point where real-time implementation becomes feasible. The modification is shown to be more stable computationally than the tradiational Ritz approach. The first concern of the paper is to describe the algorithm and establish its properties as a valid and useful numerical technique. In particular such useful properties as definiteness and reasonableness of condition are established for the method. The second part of the paper is devoted to a comparison of the new techniques with the standard procedure of numerically integrating a matrix Riccati equation to determine a feedback matrix. The new technique is shown to be significantly faster for comparable accuracy.

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Bosarge, W. E. Jr., and Johnson, O. G. Error bounds of high order accuracy for the State Regulator Problem via piecewise polynomial approximations. IBM IgPO Tech. Rep. 320.2372, Sept. 1969 (to appear, SlAM J. Control.)

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Bosarge, W. E. Jr., and Johnson, O. G. Direct method approximation to the State Regulator Control Problem using a Ritz-Trefftz suboptimal control, mM DPO Tech. Rep. 320.2377, Nov. 1969 (to appear, Trans. IEEE,)

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EDGAR TVERMEYCHUK JLAPIDUS L(2007)THE LINEAR-QUADRATIC CONTROL PROBLEM: A REVIEW OF THEORY AND PRACTICEChemical Engineering Communications10.1080/009864473089604151:2(57-76)Online publication date: 21-May-2007
https://doi.org/10.1080/00986447308960415
Meng Yao Chun-Ni Dai Ming Li Zhu-Jie Xie Chun-Hong Chen (2005)A species compete-die out (SCD) algorithm model for improving the performances of evolutionary computation in greenhouse2005 International Conference on Machine Learning and Cybernetics10.1109/ICMLC.2005.1527522(3357-3362 Vol. 6)Online publication date: 2005
https://doi.org/10.1109/ICMLC.2005.1527522
Johnson OMangin XRhyne J(2005)An interactive implementation of control theory techniques applied to Pindyck's model of the U.S. EconomyOptimization Techniques Modeling and Optimization in the Service of Man Part 110.1007/3-540-07622-0_502(676-690)Online publication date: 21-May-2005
https://doi.org/10.1007/3-540-07622-0_502
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Published In

Communications of the ACM Volume 14, Issue 6

June 1971

68 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/362604

Editor:
M. Stuart Lynn
IBM Scientific Center, Houston, TX

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 1971

Published in CACM Volume 14, Issue 6

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EDGAR TVERMEYCHUK JLAPIDUS L(2007)THE LINEAR-QUADRATIC CONTROL PROBLEM: A REVIEW OF THEORY AND PRACTICEChemical Engineering Communications10.1080/009864473089604151:2(57-76)Online publication date: 21-May-2007
https://doi.org/10.1080/00986447308960415
Meng Yao Chun-Ni Dai Ming Li Zhu-Jie Xie Chun-Hong Chen (2005)A species compete-die out (SCD) algorithm model for improving the performances of evolutionary computation in greenhouse2005 International Conference on Machine Learning and Cybernetics10.1109/ICMLC.2005.1527522(3357-3362 Vol. 6)Online publication date: 2005
https://doi.org/10.1109/ICMLC.2005.1527522
Johnson OMangin XRhyne J(2005)An interactive implementation of control theory techniques applied to Pindyck's model of the U.S. EconomyOptimization Techniques Modeling and Optimization in the Service of Man Part 110.1007/3-540-07622-0_502(676-690)Online publication date: 21-May-2005
https://doi.org/10.1007/3-540-07622-0_502
Micula GMicula SMicula GMicula S(1999)ReferencesHandbook of Splines10.1007/978-94-011-5338-6_12(383-600)Online publication date: 1999
https://doi.org/10.1007/978-94-011-5338-6_12
El-Asfouri SJohnson OMcInnis B(1976)On the problem of minimizing the volume of a vibrating cantileverQuarterly of Applied Mathematics10.1090/qam/44913334:2(203-206)Online publication date: Jul-1976
https://doi.org/10.1090/qam/449133

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A numerical scheme based on a solution of nonlinear advection-diffusion equations

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