Optimization of time delay systems by hybrid functions

A method for finding the optimal control of a linear time varying delay system with quadratic performance index is discussed. The properties of the hybrid functions which consists of block-pulse functions plus Taylor series are presented. The method is based upon expanding various time functions in the system as their truncated hybrid functions. Operational matrices of integration and delay are presented and are utilized to reduce the solution of an optimazation problem to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.