Improve Algorithms in Optimal Control for a Distributed Parameter System with Time Delay ☆

This article researches the optimal control for a distributed parameter system with time delay. One of the application of this problem is controlling the embryos heating process in the oven so that after a given time, the temperature in embryos reaches is the smallest error compared with the desired temperature. There are two point contents: Firstly, the Author has used the Laplace transform method to solve partial differential equations along with ordinary differential equation, with time delay to calculate the temperature in the embryos when knowing the power or voltage supplied to the furnace; Secondly, during the optimal experience by using numerical methods, the author has pointed out the algorithm to switch from a non-linear programming problem to linear programming problem, leading to the optimization problem is much simpler. The contents of research are proven by simulation and opens the possibility to practical applications.