This thesis is concerned with the numerical solution of optimal control problems with multiple delays in both state and control variables. Many real-life phenomena and practical systems can be modeled by various types of delay differential equations (DDEs). Typical examples are aerospace engineering, transmission lines, chemical processes, climate models, population dynamics, robotics, nuclear reactors, economics, communication networks, biological models, manufacturing processes and power systems. The optimal control problem for linear systems with delays is still open, depending on the delay type, specific system equation, criterion, etc. It is well known that except for some simple cases, it is either extremely difficult or impossible to analytically solve an optimal control problem involving multiple delays. Indeed, the presence of delay makes analysis and control design much more complicated. The application of Pontryagin’s maximum principle to the optimization of control systems with time delays, results in a system of coupled two-point boundary value problem involving both delayed and advanced terms. Therefor, the main object of all computational aspects of optimal control of time-delay systems has been to devise a methodology to avoid the solution of the mentioned two-point boundary value problem. It is worth noting that the corresponding solution to this 0cm 0cm 10pt" The purpose of this thesis is to develop a unified computational approach to effectively solve optimal control problems involving multiple delays in both state and control variables. As noted before, the analytical solution of these systems cannot be obtained solely either by piecewise constant basis functions including block-pulse functions or by continuous basis functions such as Lagrange interpolating polynomials. Combining block-pulse functions and Lagrange interpolating polynomials allows one to simultaneously make use of the best characteristics of the two mentioned bases. The excellent properties of the hybrid functions together with the associated operational matrices of delay, product and integrations are used to transform the delayed optimal control problem into a finite dimensional optimization problem whose solution is much easier than the original one. The proposed approximation scheme enables one to accurately adjust the true locations of switching points that occur in the exact response of the optimal control problem. The new method is flexible as it allows the number of the required subintervals and polynomial degrees to vary through the time interval of interest. A simple and straightforward strategy is offered for determining the required number of block-pulse functions. The appropriate value of N would greatly improve the accuracy of the proposed decomposition scheme. Several numerical examples are investigated to demonstrate the validity and applicability of the proposed approximation scheme. The method is easy to implement and provides very accurate results.