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In chapter one, a brief review of some work associated with the computational methods: direct and indirect are given for optimal control problem is discussed. Chapter two present and derives some new important properties and formulas concerning Laguerre and Hermite functions. Chapter three gives some modified algorithms are proposed depending on the pontryagin minimum principle. Chapter four describes a method for approximate the solution of OCP using state vector parameterizations. In chapter five the idea of spectral method is applied to propose four algorithms for OCP. In Chapter six Conclusions and further research directions are included.
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