Most of the direct methods solve optimal control problems with nonlinear programming solver. In this paper we propose a novel feedback control method for solving for solving affine control system, with quadratic cost functional, which makes use of only linear systems. This method is a numerical technique, which is based on the combination of Haar wavelet collocation method and successive Generalized Hamilton-Jacobi-Bellman equation. We formulate some new Haar wavelet operational matrices in order to manipulate Haar wavelet series. The proposed method has been applied to solve linear and nonlinear optimal control problems with infinite time horizon. The simulation results indicate that the accuracy of the control and cost can be improved by increasing the wavelet resolution.

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Haar wavelet collocation points method is developed to the computational solution for nonlinear Fredholm integral and integro-differential equations on interval [0, tf ] using Leibnitz-Haar wavelet collocation points method. Essential principle is transmutation of the integral equation to equivalent higher order differential equation together with initial conditions. The transmutation is carried out using the Leibniz law. Haar wavelet collocation points and its operational matrix is employed to transform the higher order differential equation to a set of algebraic equations, then resolving these equations usage MATLAB program to calculate the demanded Haar coefficients. The computational results of the proposed approach is presented in four problems and make a simulation against the accurate solution. In addition, Error analysis is exhibited the proficiency of the proposed technique and when Haar wavelet resolutions increases the results are close to the accurate solutions.

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