State analysis and optimal control of time-varying discrete systems via Haar wavelets

C. H. Hsiao; W. J. Wang

doi:10.1023/A:1021788125013

State analysis and optimal control of time-varying discrete systems via Haar wavelets

C. H. Hsiao, W. J. Wang

Department of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The state analysis and optimal control of time-varying discrete systems via Haar wavelets are the main tasks of this paper. First, we introduce the definition of discrete Haar wavelets. Then, a comparison between Haar wavelets and other orthogonal functions is given. Based upon some useful properties of the Haar wavelets, a special product matrix and a related coefficient matrix are proposed; also, a shift matrix and a summation matrix are derived. These matrices are very effective in solving our problems. The local property of the Haar wavelets is applied to shorten the calculation procedures.

Original language	English
Pages (from-to)	623-640
Number of pages	18
Journal	Journal of Optimization Theory and Applications
Volume	103
Issue number	3
DOIs	https://doi.org/10.1023/A:1021788125013
State	Published - Dec 1999

Keywords

Discrete systems
Haar wavelets
Optimal control

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10.1023/A:1021788125013

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title = "State analysis and optimal control of time-varying discrete systems via Haar wavelets",

abstract = "The state analysis and optimal control of time-varying discrete systems via Haar wavelets are the main tasks of this paper. First, we introduce the definition of discrete Haar wavelets. Then, a comparison between Haar wavelets and other orthogonal functions is given. Based upon some useful properties of the Haar wavelets, a special product matrix and a related coefficient matrix are proposed; also, a shift matrix and a summation matrix are derived. These matrices are very effective in solving our problems. The local property of the Haar wavelets is applied to shorten the calculation procedures.",

keywords = "Discrete systems, Haar wavelets, Optimal control",

author = "Hsiao, {C. H.} and Wang, {W. J.}",

note = "Funding Information: 1This research was supported in part by the National Science Council of Taiwan under Grant NSC 87-2218-E-008-011. 2Graduate Student, Department of Electrical Engineering, National Central University,Chung-Li, Taiwan, Republic of China. 3Professor, Department of Electrical Engineering, National Central University, Chung-Li, Taiwan, Republic of China.",

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N2 - The state analysis and optimal control of time-varying discrete systems via Haar wavelets are the main tasks of this paper. First, we introduce the definition of discrete Haar wavelets. Then, a comparison between Haar wavelets and other orthogonal functions is given. Based upon some useful properties of the Haar wavelets, a special product matrix and a related coefficient matrix are proposed; also, a shift matrix and a summation matrix are derived. These matrices are very effective in solving our problems. The local property of the Haar wavelets is applied to shorten the calculation procedures.

AB - The state analysis and optimal control of time-varying discrete systems via Haar wavelets are the main tasks of this paper. First, we introduce the definition of discrete Haar wavelets. Then, a comparison between Haar wavelets and other orthogonal functions is given. Based upon some useful properties of the Haar wavelets, a special product matrix and a related coefficient matrix are proposed; also, a shift matrix and a summation matrix are derived. These matrices are very effective in solving our problems. The local property of the Haar wavelets is applied to shorten the calculation procedures.

KW - Discrete systems

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KW - Optimal control

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State analysis and optimal control of time-varying discrete systems via Haar wavelets

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Keywords

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