References
References
- Haar , A . (1910) . Zur theorie der orthogonalen funktionen systeme . Math. Ann. , 69 : 331 – 371 .
- Strang , G . (1989) . Wavelets and dilation equations: a brief introduction . SIAM Review , 31 : 614 – 627 .
- Daubechies , I . (1990) . The wavelet transform, time-frequency localization and signal analysis . IEEE Transactions Information Theory , 36 : 961 – 1005 .
- Chen , CF and Hsiao , CH . (1997) . Haar wavelet method for solving lumped- and distributed-parameter systems . IEE Proceedings Control Theory and Applications Pt. D , 144 : 87 – 94 .
- Hsiao , CH and Wang , WJ . (1998) . State analysis and optimal control of linear time-varying systems via Haar wavelets . Optimal Control Applications and Methods , 19 : 423 – 433 .
- Chen , CF and Hsiao , CH . (1999) . Wavelet approach to optimising dynamic systems . IEE Proceedings Control Theory and Applications Pt. D , 146 : 213 – 219 .
- Hsiao , CH and Wang , WJ . (1999) . Optimal control of linear time-varying systems via Haar wavelets . Journal of Optimization Theory and Applications , 103 : 641 – 655 .
- Hsiao , CH and Wang , WJ . (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 .
- Wu , JL , Chen , CH and Chen , CF . (2001) . Numerical inversion of Laplace transform using Haar wavelet operational matrices . IEEE Transactions on Circuits and Systems – I: Fundamental Theory and Applications , 48 ( 1 ) : 120 – 122 .
- Akansu AN Haddad RA (1992) Multiresolution Signal Decomposition-Transforms, Subbands and Wavelets, Academic Press New York
- Schechter RS (1967) The Variational Method in Engineering, Mc Graw-Hill New York
- Kelley , HJ . (1960) . Gradient theory of optimal flight paths . ARS Journal , 30
- Bryson , AE and Denham , WF . (1962) . A steepest-ascent ethod for solving optimum programming problems . Journal of Applied Mechanics , 84
- Miele , A , Pritchard , RE and Damoulakis , JN . (1970) . Sequential gradient restoration algorithm for optimal control problems . Journal of Optimization Theory and Applications , 5
- Miele , A , Tietze , JL and Levy , AV . (1972) . Summary and comparison of gradient-restoration algorithms for optimal control problems . Journal of Optimization Theory and Applications , 10
- Miele , A . (1975) . Recent advances in gradient algorithms for optimal control problems . Journal of Optimization Theory and Applications , 17
- Chen , CF and Hsiao , CH . (1975) . A Walsh series direct method for solving variational problems . Journal of the Franklin Institute , 300 : 265 – 280 .
- Hwang , C and Shih , YP . (1983) . Laguerre series direct method for variational problems . Journal of Optimization Theory and Applications , 39 : 143 – 149 .
- Chang , RY and Wang , ML . (1983) . Shifted Legendre direct method for variational problems . Journal of Optimization Theory and Applications , 39 : 299 – 307 .
- Horng , IR and Chou , JH . (1985) . Shift Chebyshev direct method for solving variational problems . International Journal of Systems Science , 16 : 855 – 861 .
- Gelfand IM Fomin SV (1963) Calculus of Variations Englewood Cliffs N.J. Prentice-Hall
- Brewster CD (1958) Approximate Methods of Higher Analysis, Interscience New York