Finding the optimal control of linear systems via He's variational iteration method

References

• Anderson, B. D.O. , and Moor, J. B. , 1990. Optimal Control . New Jersy: Prentice-Hall, Englewood Cliffs; 1990.
   Google Scholar
• Datta, K. B. , and Mohan, B. M. , 1995. Orthogonal Functions in Systems and Control . Singapore, New Jersey, London, Hong Kong: World Scientific; 1995.
   Google Scholar
• M. Dehghan and A. Saadatmandi, Variational iteration method for solving the wave equation subject to an integral conservation condition, Chaos Solitons Fractals, in press, doi:10.1016/j.chaos.2008.06.009.
   Google Scholar
• Dehghan, M. , and Shakeri, F. , 2007. Numerical solution of a biological population model using He's variational iteration method , Comput. Math. Appl. 54 (2007), pp. 1197–1209.
   Web of Science ®Google Scholar
• Dehghan, M. , and Shakeri, F. , 2008. Application of He's variational iteration method for solving the Cauchy reaction–diffusion problem , J. Comput. Appl. Math. 214 (2008), pp. 435–446.
   Web of Science ®Google Scholar
• Dehghan, M. , and Shakeri, F. , 2008. Approximate solution of a differential equation arising in astrophysics using the variational iteration method , New Astron. 13 (2008), pp. 53–59.
   Web of Science ®Google Scholar
• Dehghan, M. , and Shakeri, F. , 2008. Use of He's homotopy perturbation method for solving a partial differential equation arising in modeling of flow in porous media , J. Porous Media 11 (2008), pp. 765–778.
   Web of Science ®Google Scholar
• M. Dehghan and F. Shakeri, Solution of parabolic integro–differential equations arising in heat conduction in materials with memory via He's variational iteration technique, Commun. Numer. Methods Eng., in press.
   Google Scholar
• M. Dehghan and F. Shakeri, Solution of an integro-differential equation arising in oscillating magnetic fields using He's homotopy perturbation method, Progress in Electromagnetic Research, PIER 78 (2008), 361–376.
   Google Scholar
• Dehghan, M. , and Shakeri, F. , 2008. The use of the decomposition procedure of Adomian for solving a delay differential equation arising in electrodynamics , Phys. Scripta 78 (2008), pp. 1–11, Aricle No. 065004.
   Web of Science ®Google Scholar
• Dehghan, M. , and Shakeri, F. , 2009. The numerical solution of the second Painlevé equation , Numer. Meth. Part. Differential Equations 25 (2009), pp. 1238–1259.
   Web of Science ®Google Scholar
• Dehghan, M. , Shakourifar, M. , and Hamidi, A. , 2009. The solution of linear and nonlinear systems of Volterra functional equations using Adomian-Pade technique , Chaos, Solitons and Fractals 39 (2009), pp. 2509–2521.
   Web of Science ®Google Scholar
• Dehghan, M. , and Tatari, M. , 2006. The use of He's variational iteration method for solving the Fokker–Planck equation , Phys. Scri. 74 (2006), pp. 310–316.
   Web of Science ®Google Scholar
• Dehghan, M. , and Tatari, M. , 2008. Identifying an unknown function in a parabolic equation with overspecified data via He's variational iteration method , Chaos Solitons Fractals 36 (2008), pp. 157–166.
   Web of Science ®Google Scholar
• Ghorbani, A. , and Saberi-Nadjafi, J. , 2009. An effective modification of He's variational iteration method , Nonlinear Anal. Real World Appl. 10 (2009), pp. 2828–2833.
   Web of Science ®Google Scholar
• He, J. H. , 1997. Variational iteration method for delay differential equations , Commun. Nonlinear Sci. Numer. Simul. 2 (4) (1997), pp. 235–236.
   Google Scholar
• He, J. H. , 1998. Approximation analytical solution for seepage flow with fractional derivatives in porous media , Comput. Meth. Appl. Mech. Eng. 167 (1998), pp. 57–68.
   Web of Science ®Google Scholar
• He, J. H. , 1999. Variational iteration method–a kind of nonlinear analytical technique: some examples , Int. J. Nonlinear Mech. 34 (1999), pp. 699–708.
   Web of Science ®Google Scholar
• He, J. H. , 2005. Homotopy perturbation method for bifurcation of non-linear problems , Int. J. Nonlinear Sci. Numer. Simul. 6 (2005), pp. 207–208.
   Web of Science ®Google Scholar
• He, J. H. , and Wu, X. H. , 2006. Construction of solitary solution and compacton-like solution by variational iteration method , Chaos, Solitons Fractals 29 (2006), pp. 108–113.
   Web of Science ®Google Scholar
• He, J. H. , 2006. Some asymptotic methods for strongly nonlinear equations , Int. J. Mod. Phys. B 20 (2006), pp. 1141–1199.
   Web of Science ®Google Scholar
• He, J. H. , 2007. The variational iteration method for eighth-order initial-boundary value problems , Phys. Scr. 76 (2007), pp. 680–682.
   Web of Science ®Google Scholar
• Inc, M. , 2007. Numerical simulation of KdV and mKdV equations with initial conditions by the variational iteration method , Chaos Solitons Fractals 34 (2007), pp. 1075–1081.
   Web of Science ®Google Scholar
• Inc, M. , 2008. The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method , J. Math. Anal. Appl. 345 (2008), pp. 476–484.
   Web of Science ®Google Scholar
• Inc, M. , 2008. Exact special solutions to the nonlinear dispersive K(2, 2, 1) and K(3, 3, 1) equations by He's variational iteration method , Nonlinear Anal. Theory Methods Appl. TMA 69 (2008), pp. 624–631.
   Web of Science ®Google Scholar
• Momani, S. , 2005. Analytical and approximate solutions of the space-and-time-fractional telegraph equations , Appl. Math. Comput. 170 (2005), pp. 1126–1134.
   Web of Science ®Google Scholar
• Momani, S. , and Abuasad, S. , 2006. Analytical approach to linear fractional partial differential equations arising in fluid mechanics , Phys. Lett. A 355 (2006), pp. 271–279.
   Web of Science ®Google Scholar
• Momani, S. , and Abuasad, S. , 2006. Application of He's variational iteration method to Helmholtz equation , Choas Solitons Fractals 27 (5) (2006), pp. 1119–1123.
   Web of Science ®Google Scholar
• Momani, S. , and Odibat, Z. , 2007. Numerical comparison of methods for solving linear differential equations of fractional order , Chaos Solitons and Fractals 31 (2007), pp. 1248–1255.
   Web of Science ®Google Scholar
• Odibat, Z. , and Momani, S. , 2006. Application of variational iteration method to nonlinear differential equations of fractional order , Int. J. Non. Sci. Num. Simul. 7 (2006), pp. 27–34.
   Web of Science ®Google Scholar
• Saadatmandi, A. , and Dehghan, M. , 2009. Variational iteration method for solving a generalized pantograph equation , Comput. Math. Appl. 58 (2009), pp. 2190–2196.
   Web of Science ®Google Scholar
• Saberi-Nadjafi, J. , and Tamamgar, M. R. , 2008. The variational iteration method: a highly promising method for solving the system of integro-differential equations , Comput. Math. Appl. 56 (2008), pp. 346–351.
   Web of Science ®Google Scholar
• Shakeri, F. , and Dehghan, M. , 2008. Numerical solution of the Klein–Gordon equation via He's variational iteration method , Nonlinear Dyn. 51 (2008), pp. 89–97.
   Web of Science ®Google Scholar
• Shakeri, F. , and Dehghan, M. , 2008. Solution of a model describing biological species living together using the variational iteration method , Math. Comput. Modell. 48 (2008), pp. 486–498.
   Web of Science ®Google Scholar
• Sweilam, N. H. , and Khader, M. M. , 2007. Variational iteration method for one dimensional nonlinear thermoelasticity , Chaos, Solitons Fractals 32 (2007), pp. 145–149.
   Web of Science ®Google Scholar
• Tatari, M. , and Dehghan, M. , 2007. On the convergence of He's variational iteration method , J. Comput. Appl. Math. 207 (2007), pp. 121–128.
   Web of Science ®Google Scholar
• Tatari, M. , and Dehghan, M. , 2007. Solution of problems in calculus of variations via He's variational iteration method , Phys. Lett. A 362 (2007), pp. 401–406.
   Web of Science ®Google Scholar
• Tatari, M. , and Dehghan, M. , 2009. Improvement of He's variational iteration method for solving system of differential equations , Comput. Math. Appl. 58 (2009), pp. 2160–2166.
   Web of Science ®Google Scholar
• S.A. Yousefi and M. Dehghan, The use of He's variational iteration method for solving variational problems, Int. J. Comput. Math. in press.
   Google Scholar
• Wang, S. Q. , and He, J. H. , 2007. Variational iteration method for solving integro-differential equations , Phys. Lett. A 376 (2007), pp. 188–191.
   Google Scholar