الفهرس 
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Abstract
A Optimal control theories are playing an increasingly important role in the design of modern systems. This role has been spurred by the demand for systems of high performance, especially as more powerful computers became readily available. The problem discussed in this thesis is concerned with the optimal solution of state and/or control constrained problems, using the parameterization echnique. The proposed approach is based on expanding the control system states using combined time polynomial with unknown coefficients (parameters) and Fourier series with also unknown coefficients (parameters). The control variables, the given constraints and the objective function are then written in terms of the unknown parameters of the system states. The developed method is simp le and resu 1 ted in a much lower cost than that obtained from the previous attempts. In this thesis, the
choice of the order of the Fourier series and the time pol ynomi a 1 is based on the accw-acy of the resu 1 t i ng so 1 ut ion. Thus, there is a comp 1 ete freedom to choose ar-bi t rary
which .1 n more accurC\te resulted orders, results. The interplay between the order choice of Fourier series and the time polynomial is a major advantage of the proposed method. Most of the previous work have dealt with either control or state constrained
but not reported cases of
both state and control constrained problems. The proposed method can deal with such prob 1 ems, wh ich represent s an important c I ass of optimal control problems, in a very simple and straight forward way. In the proposed approach, the parameterized problem is solved using any of the famous nonlinear programming techniques,
limited guessing in with a selecting
a set the of points in which time at constraints must be satisfied. A comparison between available nonlinear programming software packages is also presented in the thesis.