Mathematical Researches

Delay systems are important and it is difficult to obtain their analytical solution. Therefore, numerical methods are used to solve optimal control problems with delay systems. Solving optimal control problems using orthogonal functions has attracted much attention in recent years. Specific orthogonal functions that have been used so far in this field are the Walsh, block-pulse, and Laguerre functions. In this paper, the optimal control piecewise constant delay systems using shifted chebyshev functions are transformed into a nonlinear programming problem, so that by solving it, the approximate solution of the main problem is obtained. Numerical examples are given to evaluate the efficiency of the method.