155
Views
18
CrossRef citations to date
0
Altmetric
Original Articles

Parameter identification of linear multi-delay systems via a hybrid of block-pulse functions and Taylor’s polynomials

Pages 504-518 | Received 20 Jul 2015, Accepted 02 May 2016, Published online: 13 Jul 2016

References

  • Ardekani, B.A., Samavat, M., & Rahmani, H. (1991). Parameter identification of time-delay systems via exponential Fourier series. International Journal of Systems Science, 22, 1301–1306.
  • Belkoura, L. (2012). Identifiability and algebraic identification of time delay systems. In R. Sipahi, T. Vyhlidal, S.I. Niculescu, & P. Pepe (Eds.), Time delay systems: Methods, applications and new trends. Springer series: Lecture notes in control and information sciences (Vol. 423, pp. 103–117). Berlin: Springer.
  • Belkoura, L., & Orlov, Y. (2002). Identifiability analysis of linear delay differential systems. IMA Journal of Mathematical Control and Information, 19, 73–81.
  • Belkoura, L., Richard, J.P., & Fliess, M. (2009). Parameter estimation of systems with delayed and structured entries. Automatica, 45, 1117–1125.
  • Chen, S.L., Lai, H.C., & Ho, K.C. (2006). Identification of linear time varying systems by Haar wavelet. International Journal of Systems Science, 37, 619–628.
  • Chen, W.L. (1982). Walsh series analysis of multi-delay systems. Journal of the Franklin Institute, 313, 207–217.
  • Chen, W.L., & Shih, Y.P. (1978). Shift Walsh matrix and delay differential equations. IEEE Transactions on Automatic Control, 23, 10–23.
  • Datta, K.B., & Mohan, B.M. (1995). Orthogonal functions in systems and control. Singapore: World Scientific.
  • Driver, R.D. (1977). Ordinary and delay differential equations. New York, NY: Springer-Verlag.
  • Fornberg, B. (1998). A practical guide to pseudospectral methods. New York, NY: Cambridge University Press.
  • Ghasemi, M., & Tavassoli Kajani, M. (2011). Numerical solution of time -varying delay systems by Chebyshev wavelets. Applied Mathematical Modelling, 35, 5235–5244.
  • Haddadi, N., Ordokhani, Y., & Razzaghi, M. (2012). Optimal control of delay systems by using a hybrid functions approximation. Journal of Optimization Theory and Applications, 153, 338–356.
  • Horng, I.R., & Chou, J.H. (1985). Analysis and parameter identification of time-delay systems via Chebyshev series. International Journal of Control, 41(5), 1221–1234.
  • Horng, I.R., & Chou, J.H. (1986). Analysis and parameter identification of time-delay systems via shifted Jacobi polynomials. International Journal of Control, 44, 935–942.
  • Hwang, C., & Chen, M.Y. (1985). Analysis and parameter identification of time-delay systems via shifted Legendre polynomials. International Journal of Control, 41(2), 403–415.
  • Jiang, Z.H., & Schaufelberger, W. (1992). Block-pulse functions and their applications in control systems. Berlin: Springer-Verlag.
  • Kreyszig, E. (1978). Introductory functional analysis with applications. New York, NY: John Wiley and Sons.
  • Lakshmanan, M., & Senthilkumar, D.V. (2010). Dynamics of nonlinear time-delay systems. Berlin: Springer.
  • Lancaster, P. (1969). Theory of matrices. New York, NY: Academic Press.
  • Malek-Zavarei, M., & Jamshidi, M. (1987). Time delay systems: Analysis, optimization and applications ( North-Holland Systems and Control Series). New York, NY: Elsevier Science.
  • Marzban, H.R., Hoseini, S.M., & Razzaghi, M. (2009). Solution of Volterra’s population model via block-pulse functions and Lagrange interpolating polynomials. Mathematical Methods in the Applied Sciences, 32, 127–134.
  • Marzban, H.R., & Razzaghi, M. (2000). Direct method for variational problems via hybrid of block-pulse and Chebyshev functions. Mathematical Problems in Engineering, 6, 85–97.
  • Marzban, H.R., & Razzaghi, M. (2004). Optimal control of linear delay systems via hybrid of block-pulse and Legendre polynomials. Journal of the Franklin Institute, 341, 279–293.
  • Marzban, H.R., & Razzaghi, M. (2006). Analysis of time delay systems via hybrid of block-pulse functions and Taylor’s series. Journal of Vibration and Control, 17, 1455–1468.
  • Marzban, H.R., & Razzaghi, M. (2006). Solution of multi-delay systems using hybrid of block-pulse functions and Taylor’s series. Journal of Sound and Vibration, 292, 954–963.
  • Marzban, H.R., & Razzaghi, M. (2010). Rationalized Haar approach for nonlinear constrained optimal control problems. Applied Mathematical Modelling, 34, 174–183.
  • Marzban, H.R., & Shahsiah, M. (2011). Solution of piecewise constant delay systems using hybrid of block-pulse and Chebyshev polynomials. Optimal Control Applications and Methods, 16, 647–659.
  • Marzban, H.R., Tabrizidooz, H.R., & Razzaghi, M. (2011). A composite collocation method for the nonlinear mixed Volterra–Fredholm–Hammerstein integral equations. Communications in Nonlinear Science and Numerical Simulation, 16, 1186–1194.
  • Mohammadzadeh, R., & Lakestani, M. (2015). Analysis of time-varying delay systems by hybrid of block-pulse functions and bioorthogonal multiscaling functions. International Journal of Control, 88(12), 2444–2456.
  • Smith, H. (2010). An introduction to delay differential equations with applications to the life sciences ( Texts in Applied Mathematics). Berlin: Springer.
  • Wang, M.L., Jan, Y.J., & Chang, R.Y. (1987). Analysis and parameter identification of time-delay linear systems via generalized orthogonal polynomials. International Journal of Systems Science, 18(9), 1645–1658.
  • Yang, C.Y., & Chen, C.K. (1987a). Analysis and parameter identification of time-delay systems via polynomial series. International Journal of Control, 46(1), 111–127.
  • Yang, C.Y., & Chen, C.K. (1987b). Analysis and parameter identification of time-delay systems via Taylor series. International Journal of Systems Science, 18(7), 1347–1353.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.