The use of rationalized Haar wavelet collocation method for solving optimal control of Volterra integral equations

In this paper, an efficient method based on rationalized Haar (RH) wavelets is proposed for the numerical solution of optimal control problem for systems governed by Volterra integral equations with a quadratic performance index. Many problems in economics, biology, epidemiology and memory effects can be modeled as Volterra control problems. The main advantage of the RH wavelet is based on its efficiency and simple applicability. The properties of RH wavelets are represented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the solution of the optimization problem to a nonlinear programming one to which well-developed algorithms may be applied. The convergence analysis of the method and illustrative examples are included to demonstrate the validity and applicability of the technique.