Robustness of operational matrices of differentiation for solving state-space analysis and optimal control problems

Abstract and Applied Analysis

Volumn 2013, Issue , 2013, Pages

  Tohidi, Emran ^a   Soleymani, F ^a   Kilicman, Adem ^b  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b UNIVERSITY PUTRA MALAYSIA   (Malaysia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84877248740     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2013/535979     Document Type: Article

References (32)

1. Corrington M. S., Solution of differential and integral equations with Walsh functions. IEEE Transactions Circuit Theory 1973 CT-20 5 470 476 2-s2.0-0015662698
2. Chen C. F., Hsiao C. H., Time-domain synthesis via Walsh functions. Proceedings of the Institution of Electrical Engineers 1975 122 5 565 570 2-s2.0-0016509362
3. Chen C. F., Hsiao C. H., WALSH series analysis in optimal control. International Journal of Control 1975 21 6 881 897 2-s2.0-0016521928
4. Hsu N. S., Cheng B., Analysis and optimal control of time-varying linear systems via block-pulse functions. International Journal of Control 1981 33 6 1107 1122 10.1080/00207178108922979 MR624174 ZBL0464.93027 (Pubitemid 12425981)
5. Hwang C., Shih Y. P., Laguerre series direct method for variational problems. Journal of Optimization Theory and Applications 1983 39 1 143 149 10.1007/BF00934611 MR693680 ZBL0481.49005 (Pubitemid 13506531)
6. Elnagar G. N., State-control spectral Chebyshev parameterization for linearly constrained quadratic optimal control problems. Journal of Computational and Applied Mathematics 1997 79 1 19 40 10.1016/S0377-0427(96) 00134-3 MR1437967 ZBL0871.65054 (Pubitemid 127424711)
7. Paraskevopoulos P. N., Legendre series approach to identification and analysis of linear systems. Institute of Electrical and Electronics Engineers 1985 30 6 585 589 10.1109/TAC.1985.1103992 MR789333 ZBL0559.93041 (Pubitemid 15597630)
8. Kekkeris G. Th., Paraskevopoulos P. N., Hermite series approach to optimal control. International Journal of Control 1988 47 2 557 567 10.1080/00207178808906031 MR929175 ZBL0636.93036 (Pubitemid 18580866)
9. Paraskevopoulos P. N., Sparis P. D., Mouroutsos S. G., The Fourier series operational matrix of integration. International Journal of Systems Science 1985 16 2 171 176 10.1080/00207728508926663 MR786738 ZBL0558.44004 (Pubitemid 15478257)
10. Doha E. H., Bhrawy A. H., Saker M. A., Integrals of Bernstein polynomials: an application for the solution of high even-order differential equations. Applied Mathematics Letters 2011 24 4 559 565 10.1016/j.aml.2010.11. 013 MR2749745 ZBL1236.65091
11. Paraskevopoulos P. N., Sklavounos P. G., Georgiou G. Ch., The operational matrix of integration for Bessel functions. Journal of the Franklin Institute 1990 327 2 329 341 10.1016/0016-0032(90)90026-F MR1042680 ZBL0717.93012
12. Bhrawy A. H., Tohidi E., Soleymani F., A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals. Applied Mathematics and Computation 2012 219 2 482 497 10.1016/j.amc.2012.06.020 MR2956980
13. Bhrawy A. H., Al-Shomrani M. A., A shifted Legendre spectral method for fractional order multi point boundary value problems. Advances in Differerence Equations 2012 2012 article 8
14. Doha E. H., Bhrawy A. H., Ezz-Eldien S. S., A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order. Computers & Mathematics with Applications 2011 62 5 2364 2373 10.1016/j.camwa.2011.07.024 MR2831698 ZBL1231.65126
15. Gülsu M., Gürbüz B., Öztürk Y., Sezer M., Laguerre polynomial approach for solving linear delay difference equations. Applied Mathematics and Computation 2011 217 15 6765 6776 10.1016/j.amc.2011.01. 112 MR2775723 ZBL1211.65166
16. Sezer M., yalçinbaş S., Şahin N., Approximate solution of multi-pantograph equation with variable coefficients. Journal of Computational and Applied Mathematics 2008 214 2 406 416 10.1016/j.cam.2007.03. 024 MR2398342 ZBL1135.65345 (Pubitemid 351241078)
17. Tohidi E., Legendre approximation for solving linear HPDEs and comparison with Taylor and Bernoulli matrix methods. Applied Mathematics 2012 3 5 410 416 10.4236/am.2012.35063 MR2926642
18. Tohidi E., Bhrawy A. H., Erfani Kh., A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation. Applied Mathematical Modelling 2013 37 6 4283 4294 10.1016/j.apm.2012.09.032
19. Tohidi E., Bernoulli matrix approach for solving two dimensional linear hyperbolic partial differential equations with constant coefficients. American Journal of Computational and Applied Mathematics 2012 2 4 136 139 10.5923/j.ajcam.20120204.01
20. Toutounian F., Tohidi E., Shateyi S., A collocation method based on Bernoulli operational matrix for solving high order linear complex differential equations in a rectangular domain. Abstract and Applied Analysis 2013 823098
21. Toutounian F., Tohidi E., Kiliçman A., Fourier operational matrices of differentiation and transmission: introduction and applications. Abstract and Applied Analysis 2013 198926
22. Yalçinbaş S., Aynigül M., Sezer M., A collocation method using Hermite polynomials for approximate solution of pantograph equations. Journal of the Franklin Institute 2011 348 6 1128 1139 10.1016/j.jfranklin.2011.05.003 MR2803650 ZBL1221.65187
23. Yousefi S. A., Behroozifar M., Operational matrices of Bernstein polynomials and their applications. International Journal of Systems Science 2010 41 6 709 716 10.1080/00207720903154783 MR2662740 ZBL1195.65061
24. Yuzbasi S., Bessel polynomial solutions of linear differential, integral and integro-differential equations [M.S. thesis] 2009 Graduate School of Natural and Applied Sciences, Mugla University
25. Samadi O. R. N., Tohidi E., The spectral method for solving systems of Volterra integral equations. Journal of Applied Mathematics and Computing 2012 40 1-2 477 497 10.1007/s12190-012-0582-8 MR2965344
26. Tohidi E., Samadi O. R. N., Optimal control of nonlinear Volterra integral equations via Legendre polynomials. IMA Journal of Mathematical Control and Information 2013 30 1 67 83
27. Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mishchenko E. F., The Mathematical Theory of Optimal Processes 1962 Wiley Interscience MR0166037
28. Geering H. P., Optimal Control with Engineering Applications 2007 Berlin, Germany Springer
29. Tohidi E., Samadi O. R. N., Farahi M. H., Legendre approximation for solving a class of nonlinear optimal control problems. Journal of Mathematical Finance 2011 1 8 13 10.4236/jmf.2011.11002.2011
30. Maleknejad K., Almasieh H., Optimal control of Volterra integral equations via triangular functions. Mathematical and Computer Modelling 2011 53 9-10 1902 1909 10.1016/j.mcm.2011.01.017 MR2782893 ZBL1219.49026
31. Wang M. L., Chang R. Y., Yang S. Y., Analysis and optimal control of time-varying systems via generalized orthogonal polynomials. International Journal of Control 1986 44 4 895 910 2-s2.0-0022803444
32. Kung F. C., Lee H., Solution of linear state-space equations and parameter estimation in feedback systems using laguerre polynomial expansion. Journal of the Franklin Institute 1982 314 6 393 403 2-s2.0-0020246838