ABSTRACT
Engineering systems often contain delayed elements such as recycle streams, transportation lags, and time delays associated with the measurement of output variables. These time delays can have significant effect on the control of the system under consideration, so it is important to incorporate them into the mathematical model. This gives rise to differential equations with delayed arguments. The first attempt to use iterative dynamic programming with time-delay systems was made by S. Dadebo and R. Luus, who used piecewise constant control policy, and obtained good results with several problems. The work by Luus et al. shows that a good way of overcoming such difficulty is to use the Taylor series expansion for the delay terms to convert the given system into a nondelay system for which the optimal control policy can be readily established. The optimal control policy for the nondelay system provides the starting control policy for the time-delay system.
