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This paper deals with an optimal control problem with quadratic cost for a class of bilinear systems using the orthogonal functions technique. The main idea of this technique is that it reduces the problem to solving a system of algebraic equations, thus simplifying the problem. The control variable and the state variables are approximated by block pulse functions series. Then the system dynamics is transformed into systems of algebraic equations. Finally, numerical results are given to illustrate the proposed method. [ABSTRACT FROM AUTHOR]