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State Analysis and Optimal Control of Time-Varying Discrete Systems via Haar Wavelets

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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.

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Authors and Affiliations

  1. Department of Electrical Engineering, National Central University, Chung-Li, Taiwan, Republic of China

    C. H. Hsiao (Graduate Student)

  2. Department of Electrical Engineering, National Central University, Chung-Li, Taiwan, Republic of China

    W. J. Wang (Professor)

Authors
  1. C. H. Hsiao
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  2. W. J. Wang
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Hsiao, C.H., Wang, W.J. State Analysis and Optimal Control of Time-Varying Discrete Systems via Haar Wavelets. Journal of Optimization Theory and Applications 103, 623–640 (1999). https://doi.org/10.1023/A:1021788125013

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  • DOI: https://doi.org/10.1023/A:1021788125013

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