제어로봇시스템학회논문지 (Journal of Institute of Control, Robotics and Systems)

  • 제14권12호
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  • Pages.1270-1277
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  • 2008
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  • 1976-5622(pISSN)
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  • 2233-4335(eISSN)
제어로봇시스템학회 (Institute of Control, Robotics and Systems)
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웨이블릿 및 시스템 분할을 이용한 특이섭동 선형 시스템 해석

Wavelet-based Analysis for Singularly Perturbed Linear Systems Via Decomposition Method

  • 김범수 (경상대학교 기계항공공학부, 해양산업연구소) ;
  • 심일주 (대림대학 자동화시스템과)
  • 발행 : 2008.12.01
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초록

A Haar wavelet based numerical method for solving singularly perturbed linear time invariant system is presented in this paper. The reduced pure slow and pure fast subsystems are obtained by decoupling the singularly perturbed system and differential matrix equations are converted into algebraic Sylvester matrix equations via Haar wavelet technique. The operational matrix of integration and its inverse matrix are utilized to reduce the computational time to the solution of algebraic matrix equations. Finally a numerical example is given to demonstrate the validity and applicability of the proposed method.

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참고문헌

  1. Z. Gajic and M.T. Lim, Optimal Control Of Singularly Perturbed Linear Systems And Applications, Marcel Dekker, New York, 2001
  2. H. R. Karimi, P. J. Maralani, B. Moshiri, and B. Lohmann, 'Numerically efficient approximations to the optimal control of linear singularly perturbed systems based on Haar wavelets,' Int. J. of Computer Mathematics, vol. 82, pp. 495-507, 2005 https://doi.org/10.1080/00207160512331323407
  3. R. S. Stankovic and B. J. Falkowski, 'The Haar wavelet transform: its status and achievements,' Computers and Electrical Engineering, vol. 29, no. 1, pp. 25-44, 2003 https://doi.org/10.1016/S0045-7906(01)00011-8
  4. C. F. Chen and C. H. Hsiao, 'Haar wavelet method for solving lumped and distributed-parameter systems,' IEE Proc. Control Theory Appl. vol. 144, pp. 87-94, 1997 https://doi.org/10.1049/ip-cta:19970702
  5. M. Ohkita and Y. Kobayashi, 'An application of rationalized Haar functions to solution of linear differential equations.' IEEE Trans. Circuits Systems I. Fund. Theory Appl. vol. 9, pp. 853-862, 1986
  6. C. H. Hsiao and W. J. Wang, 'State analysis and parameter estimation of bilinear systems via Haar wavelets,' IEEE Trans. Circuits Systems I. Fundam. Theory Appl. vol. 47, pp. 246-250, 2000 https://doi.org/10.1109/81.828579
  7. B. S. Kim, I. J. Shim, B. K. Choi, and J. H. Jeong, 'Wavelet based control for linear systems via reduced order Sylvester equation,' The 3rd Int. Conf. on Cooling and Heating Technologies, pp. 239-244, 2007
  8. B. S. Kim and I. J. Shim 'Haar wavelet-based control for HVAC systems,' 2007 Int. Sym. On Advanced Intelligent Systems, pp. 647-650, 2007
  9. C. H. Hsiao, 'Solution of variational problems via Haar orthonormal wavelet direct method,' Int. J. Comput. Math, vol. 81, pp. 871-887, 2004 https://doi.org/10.1080/00207160410001712323
  10. A. Haar, 'Zur Theorie der orthogonaler Funktionensysteme,' Math. Ann. vol. 69, pp. 331-371, 1910 https://doi.org/10.1007/BF01456326
  11. K. W. Chang, 'Singular perturbations of a general boundary value problems,' SIAM J. Math. Anal., vol. 3, pp. 520-526, 1972 https://doi.org/10.1137/0503050
  12. J. Brewer, 'Kronecker products and matrix calculus in system theory,' IEEE Trans. on Circuits and Systems, vol. 25, pp. 772-781, 1978 https://doi.org/10.1109/TCS.1978.1084534
  13. F. Ding and T.W. Chen, 'Gradient based iterative algorithms for solving a class of matrix equations,' IEEE Tran. Automa. Contr., vol. 50, pp. 1216-1221, 2005 https://doi.org/10.1109/TAC.2005.852558
  14. G. H. Golub, S. Nash, and C. Van Loan, 'A Hessenberg-Schur Method for the Problem AX + XB = C,' IEEE Trans. Automa. Contr., vol. 24, pp. 909-913, 1979 https://doi.org/10.1109/TAC.1979.1102170
  15. G. Freiling, 'A survey of nonsymmetric Riccati equations,' Linear Algebra Appl., pp. 243-270, 2002
  16. Y. Arkun and S. Ramakrishnan, 'Bounds on the optimum quadratic cost of structure-constrained controllers,' IEEE Tran. Automa. Contr., vol. 28, pp. 924- 927, 1983 https://doi.org/10.1109/TAC.1983.1103343