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In chapter one, a brief review of some work associated with the computational methods to treat the optimal control problems is presented. Chapter two, gives some new important properties and formulas of chebyshev polynomials of first and second kinds. The idea of spectral method is applied in chapter three to solve quadratic optimal control problems with the aid of Chebyshev polynomials convergence criteria for the proposed algorithms are also included in this chapter. Conclusions and further research direction are included in chapter four.