{"title":"Optimal Control of Volterra Integro-Differential Systems Based On Legendre Wavelets and Collocation Method","authors":"Khosrow Maleknejad, Asyieh Ebrahimzadeh","volume":91,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1040,"pagesEnd":1045,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9998763","abstract":"
In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential
\r\n(VID) equation is considered. The method is developed by means
\r\nof the Legendre wavelet approximation and collocation method. The
\r\nproperties of Legendre wavelet together with Gaussian integration
\r\nmethod are utilized to reduce the problem to the solution of nonlinear
\r\nprogramming one. Some numerical examples are given to confirm the
\r\naccuracy and ease of implementation of the method.<\/p>\r\n","references":"[1] E. Tohidi and O. R. N. Samadi, Optimal control of nonlinear Volterra\r\nintegral equations via Legendre polynomials, IMA J. Math. Control Info,\r\nvol. 30, no. 3, pp. 67-83, July 2012.\r\n[2] T. S. Angell, On the optimal control of systems governed by nonlinear\r\nVolterra equations, J. Optim. Theory Appl., vol. 19, no. 1, pp. 29-45,\r\n1976.\r\n[3] A. H. Borzabadi, A. Abbasi, and O. S. Fard, Approximate optimal control\r\nfor a class of nonlinear Volterra integral equation, J. Am. Sci., vol. 6,\r\nno. 11, pp. 1017-1021, 2010.\r\n[4] S. A. Belbas, A reduction method for optimal control of Volterra integral\r\nequations, Appl. Math. Comput, vol. 197, no. 2, pp. 880-890, April 2008.\r\n[5] G. N Elnegar Optimal control computation for integro-differential\r\naerodynamic equations, Math. Method Appl. Sci., vol. 21, no. 7,\r\npp. 653-664, May. 1998.\r\n[6] S. A. 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