Solving of optimal control problem of parabolic PDEs in exploitation of oil by iterative dynamic programming

Optimal control problem for the exploitation of oil is investigated. The optimal control problem under consideration in this paper is governed by weak coupled parabolic PDEs and involves with point wise state and control constrained. In this paper we use iterative dynamic programming method for solving optimal control problem. In this method we have broken up the problem into a number of stages and assumed that the performance index could always be expressed explicitly in terms of the state variables at the last stage. This provided a scheme where we could proceed backwards in a systematic way, carrying out optimization at each stage. In this method we use from finite-difference method for obtaining the approximate trajectory at each stage and finally we obtain the optimal control for the original problem.