Analysis of Multi-delay and Piecewise Constant Delay Systems by Hybrid Functions Approximation

详细信息    查看全文

• 作者：S. Mashayekhi ; M. Razzaghi…
• 关键词：Hybrid ; Bernoulli polynomials ; Block ; pulse ; Delay systems
• 刊名：Differential Equations and Dynamical Systems
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：24
• 期：1
• 页码：1-20
• 全文大小：515 KB
• 参考文献：1.Malek-Zavarei, M., Jamshidi, M.: Time Delay Systems: Analysis Optimization and Applications North-Holland Systems and Control Series. Elsevier, New York (1987)MATH
  2.Cai, G., Huang, J.: Optimal control method with time delay in control. J. Sound Vib. 251, 383–394 (2002)CrossRef MathSciNet MATH
  3.Zhang, J., Knospe, C.R., Tsiotras, P.: New results for the analysis of linear systems with time-invariant delays. Int. J. Robust Nonlinear Control 13, 1149–1175 (2003)CrossRef MathSciNet MATH
  4.Abdulaziz, O., Hashim, I., Chowdhury, M.S.H.: Solving variational problems by homotopy perturbation method. Int. J. Numer. Methods Eng. 75, 709–721 (2008)CrossRef MathSciNet MATH
  5.Marzban, H.R., Shahsiah, M.: Solution of piecewise constant delay systems using hybrid of block-pulse and Chebyshev polynomials. Optim. Control Appl. Methods 32, 647–659 (2010)CrossRef MathSciNet
  6.Hwang, C., Shih, Y.P.: Optimal control of delay systems via block pulse functions. J. Optim. Theory Appl. 45, 101–112 (1985)CrossRef MathSciNet MATH
  7.Palanisamy, K.R., Rao, G.P.: Optimal control of linear systems with delays in state and control via Wash functions. IEE Proc. D. Control Theory Appl. 130, 300–312 (1983)CrossRef MATH
  8.Hwang, C., Shih, Y.P.: Laguerre series direct method for variational problems. J. Optim. Theory Appl. 39, 143–149 (1983)CrossRef MathSciNet MATH
  9.Horng, I.R., Chou, J.H.: Shifted Chebyshev direct method for solving variational problems. Int. J. Syst. Sci. 16, 855–861 (1985)CrossRef MathSciNet MATH
  10.Chang, R.Y., Wang, M.L.: Shifted Legendre direct method for variational problems. J. Optim. Theory App. 39, 299–307 (1983)CrossRef MathSciNet MATH
  11.Razzaghi, M.: Optimal control of linear time-varying systems via Fourier series. J. Optim. Theory Appl. 65, 375–384 (1990)CrossRef MathSciNet MATH
  12.Razzaghi, M., Razzaghi, M.: Instabilities in the solution of a heat conduction problem using Taylor series and alternative approaches. J. Frankl. Inst. 326, 683–690 (1989)CrossRef MATH
  13.Razzaghi, M., Marzban, H.R.: A hybrid domain analysis for systems with delays in state and control. Math. Probl. Eng. 7, 337–353 (2001)CrossRef MathSciNet MATH
  14.Marzban, H.R., Razzaghi, M.: Solution of time-varying delay systems by hybrid functions. Math. Comput. Simul. 64, 597–607 (2004)CrossRef MathSciNet
  15.Marzban, H.R., Razzaghi, M.: Analysis of time-delay systems via hybrid of block-pulse functions and Taylor series. J. Vib. Control 11, 1455–1468 (2005)CrossRef MathSciNet MATH
  16.Wang, X.T., Li, Y.M.: Numerical solutions of integro differential systems by hybrid of general block-pulse functions and the second Chebyshev polynomials. Appl. Math. Comput. 209, 266–272 (2009)CrossRef MathSciNet MATH
  17.Singh, V.K., Pandey, R.K., Singh, S.: A stable algorithm for Hankel transforms using hybrid of block-pulse and Legendre polynomials. Comput. Phy. Commun. 181, 1–10 (2010)CrossRef MathSciNet MATH
  18.Costabile, F., Dellaccio, F., Gualtieri, M.T.: A new approach to Bernoulli polynomials. Rend. Mat. Ser. VII 26, 1–12 (2006)MathSciNet MATH
  19.Arfken, G.: Mathematical Methods for Physicists, 3rd edn. Academic press, San Diego (1985)
  20.Kreyszig, E.: Introductory Functional Analysis with Applications. Wiley, New York (1978)MATH
  21.Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods, Fundamentals in Single Domains. Springer, Berlin (2006)MATH
  22.Marzban, H.R., Tabrizidooz, H.R., Razzaghi, M.: A composite collocation method for the nonlinear mixed Volterra–Fredholm–Hammerstein integral equations. Commun. Nonlinear Sci. Numer. Simul. 16, 1186–1194 (2011)CrossRef MathSciNet MATH
  23.Mashayekhi, S., Ordokhani, Y., Razzaghi, M.: Hybrid functions approach for nonlinear constrained optimal control problems. Commun. Nonlinear Sci. Numer. Simul. 17, 1831–1843 (2012)CrossRef MathSciNet MATH
  24.Mashayekhi, S., Ordokhani, Y., Razzaghi, M.: Hybrid functions approach for optimal control of systems described by integro-differential equations. Appl. Math. Model. 37, 3355–3368 (2013)CrossRef MathSciNet
  25.Lancaster, P.: Theory of Matrices. Academic Press, New York (1969)MATH
  26.Datta, K.B., Mohan, B.M.: Orthogonal Functions in Systems and Control. World Scientific, Singapore (1995)CrossRef MATH
  
• 作者单位：S. Mashayekhi (1)
  M. Razzaghi (1)
  M. Wattanataweekul (2)
  
  1. Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS , 39762, USA
  2. Department of Mathematics, Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubonratchathani , 34190, Thailand
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  
• 出版者：Springer India
• ISSN：0974-6870

文摘

In this paper, a new numerical method for solving multi-delay and piecewise constant delay systems is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration, product and delay are given. These matrices are then utilized to reduce the solution of multi-delay systems and the piecewise constant delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. Keywords Hybrid Bernoulli polynomials Block-pulse Delay systems