A computational method for optimal control problem of time-varying state-delayed systems by Haar wavelets

References

• Horng , I. R. and Chou , J. H. 1985 . Analysis, parameter estimation and optimal control of time-delay systems via Chebyshev series . International Journal of Control , 41 : 1221 – 1234 .
   Web of Science ®Google Scholar
• Karimi , H. R. , Jabehdar Maralani , P. , Lohmann , B. and Moshiri , B. 2005 . H ∞ control of linear parameter-dependent state-delayed systems using polynomial parameter-dependent quadratic functions . International Journal of Control , 78 : 254 – 263 .
   Google Scholar
• Karimi , H. R. and Yazdanpanah , M. J. 2005 . Robust control for a class of uncertain state-delayed singularly perturbed systems . Asian Journal of Control , 7 : 202 – 208 .
   Google Scholar
• Kung , F. C. and Lee , H. 1983 . Solution and parameter estimation of in linear time-invariant delay systems using Laguerre polynomial expansion . Transactions of the ASME Journal of Dynamic Systems and Measurement Control , 105 : 297 – 301 .
   Web of Science ®Google Scholar
• Lee , H. and Kung , F. C. 1985 . Shifted Legendre series solution and parameter estimation of linear delayed systems . International Journal of Systems Science , 16 : 1249 – 1256 .
   Web of Science ®Google Scholar
• Marzban , H. R. and Razzaghi , M. 2004 . Solution of time-varying delay systems by hybrid functions . Mathematics and Computers in Simulation , 64 : 597 – 607 .
   Web of Science ®Google Scholar
• Rao , G. P. and Sivakumar , L. Analysis and synthesis of dynamic systems containing time-delays via block-pulse functions . Proceedings of the IEE , 125 1064 – 1068 .
   Google Scholar
• Burrus , C. S. , Gopinath , R. A. and Guo , H. 1988 . Introduction to Wavelets and Wavelet Transforms , Upper Saddle River, NJ : Prentice Hall .
   Google Scholar
• Chen , C. F. and Hsiao , C. H. 1997 . Haar wavelet method for solving lumped and distributed-parameter systems . IEE Proceedings of Control Theory and Applications , 144 : 87 – 94 .
   Google Scholar
• Hsiao , C. H. and Wang , W. J. 2000 . State analysis and parameter estimation of bilinear systems via Haar wavelets . IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications , 47 : 246 – 250 .
   Google Scholar
• Karimi , H. R. , Lohmann , B. , Jabehdar Maralani , P. and Moshiri , B. 2004 . A computational method for solving optimal control and parameter estimation of linear systems using Haar wavelets . International Journal of Computer Mathematics , 81 : 1121 – 1132 .
   Web of Science ®Google Scholar
• Karimi , H. R. , Jabehdar Maralani , P. , Moshiri , B. and Lohmann , B. 2005 . Numerically efficient approximations to the optimal control of linear singularly perturbed systems based on Haar wavelets . International Journal of Computer Mathematics , 82 : 495 – 507 .
   Web of Science ®Google Scholar
• Karimi , H. R. , Moshiri , B. , Lohmann , B. and Jabehdar Maralani , P. 2005 . Haar wavelet-based approach for optimal control of second-order linear systems in time domain . Journal of Dynamical and Control Systems , 11 : 237 – 252 .
   Web of Science ®Google Scholar
• Ohkita , M. and Kobayashi , Y. 1986 . An application of rationalized Haar functions to solution of linear differential equations . IEEE Transactions on Circuits and Systems , 9 : 853 – 862 .
   Google Scholar
• Razzaghi , M. and Ordokhani , Y. 2002 . A rationalized Haar functions method for nonlinear Fredholm–Hammerstein integral equations . International Journal of Computer Mathematics , 79 : 333 – 343 .
   Web of Science ®Google Scholar
• Chen , C. F. and Hsiao , C. H. 1965 . A state-space approach to Walsh series solution of linear systems . International Journal of Systems Science , 6 : 833 – 858 .
   Web of Science ®Google Scholar
• Rao , G. P. 1983 . Piecewise Constant Orthogonal Functions and their Application to Systems and Control , Berlin : Springer-Verlag .
   Google Scholar
• Hwang , C. and Shin , Y. P. 1981 . Laguerre operational matrices for fractional calculus and applications . International Journal of Control , 34 : 557 – 584 .
   Web of Science ®Google Scholar
• Chang , R. Y. and Wang , M. L. 1984 . Legendre polynomials approximation to dynamical linear state-space equations with initial and boundary value conditions . International Journal of Control , 40 : 215 – 232 .
   Web of Science ®Google Scholar
• Razzaghi , M. and Razzaghi , M. 1988 . Fourier series direct method for variational problems . International Journal of Control , 48 : 887 – 895 .
   Web of Science ®Google Scholar
• Haar , A. 1910 . Zur Theorie der orthogonalen Funktionensysteme . Mathematische Annalen , 69 : 331 – 371 .
   Google Scholar
• Reis , J. J. , Lynch , R. T. and Butman , J. 1976 . “ Adaptive Haar transform video bandwith reduction system for RPVs ” . In Proceedings of the SPIE Annual Meeting, San Diego, CA 24 – 35 .
   Google Scholar
• Banks , H. T. and Burns , J. A. 1978 . Hereditary control problems: numerical methods based on averaging approximations . SIAM Journal of Control and Optimization , 16 : 169 – 208 .
   Web of Science ®Google Scholar