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Optimal Control of Linear Time-Varying Systems via Haar Wavelets

Author

Listed:
  • C. H. Hsiao

    (National Central University)

  • W. J. Wang

    (National Central University)

Abstract

This paper introduces the application of Haar wavelets to the optimal control synthesis for linear time-varying systems. Based upon some useful properties of Haar wavelets, a special product matrix, a related coefficient matrix, and an operational matrix of backward integration are proposed to solve the adjoint equation of optimization. The results obtained by the proposed Haar approach are almost the same as those obtained by the conventional Riccati method.

Suggested Citation

  • C. H. Hsiao & W. J. Wang, 1999. "Optimal Control of Linear Time-Varying Systems via Haar Wavelets," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 641-655, December.
    • Handle: RePEc:spr:joptap:v:103:y:1999:i:3:d:10.1023_a:1021740209084
    DOI: 10.1023/A:1021740209084
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    References listed on IDEAS

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    1. Hsiao, Chun-Hui, 1997. "State analysis of linear time delayed systems via Haar wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(5), pages 457-470.
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    Citations

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    Cited by:

    1. R. Dai & J. E. Cochran, 2009. "Wavelet Collocation Method for Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 265-278, November.
    2. Hsiao, Chun-Hui, 2004. "Haar wavelet direct method for solving variational problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(5), pages 569-585.
    3. Monika Garg & Lillie Dewan, 2012. "Non-recursive Haar Connection Coefficients Based Approach for Linear Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 320-337, May.
    4. Hsiao, Chun-Hui & Wang, Wen-June, 2001. "Haar wavelet approach to nonlinear stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(6), pages 347-353.
    5. T. Binder & L. Blank & W. Dahmen & W. Marquardt, 2001. "Iterative Algorithms for Multiscale State Estimation, Part 1: Concepts," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 501-527, December.
    6. C. H. Hsiao & W. J. Wang, 1999. "State Analysis and Optimal Control of Time-Varying Discrete Systems via Haar Wavelets," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 623-640, December.
    7. Hsiao, C.H., 2004. "Haar wavelet approach to linear stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(5), pages 561-567.
    8. Tian, Yongge & Herzberg, Agnes M., 2006. "A-minimax and D-minimax robust optimal designs for approximately linear Haar-wavelet models," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2942-2951, June.

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    Keywords

    Optimal control; Haar wavelets;

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