Solving the optimal control problem of the parabolic PDEs in exploitation of oil

Abstract

In this paper, the optimal control problem is governed by weak coupled parabolic PDEs and involves pointwise state and control constraints. We use measure theory method for solving this problem. In order to use the weak solution of problem, first problem has been transformed into measure form. This problem is reduced to a linear programming problem. Then we obtain an optimal measure which is approximated by a finite combination of atomic measures. We find piecewise-constant optimal control functions which are an approximate control for the original optimal control problem.

Adaptive Control Based on Passive Identifier for Uncertain Coupled Parabolic Equations

“…Before proceeding the proof, the following equations derived from (7) are given which will be used in the later proof:…”

“…Controllers design with different control objectives have been one of the important parts of the controls for coupled parabolic equations. Multiple classes of control problems have been investigated for different coupled parabolic equations (see [7]- [17] and the references therein). Specifically, optimal control problems have been investigated in [7], [8] for two classes of coupled parabolic equations arise in exploitation of oil and population system, respectively.…”

“…Multiple classes of control problems have been investigated for different coupled parabolic equations (see [7]- [17] and the references therein). Specifically, optimal control problems have been investigated in [7], [8] for two classes of coupled parabolic equations arise in exploitation of oil and population system, respectively. Output regulation for a class of coupled linear parabolic partial integro-differential equations (PIDEs) has been investigated in [9].…”

Solving the Optimal Control of Linear Systems via Homotopy Perturbation Method

“…In [9] the problem is solved by converting the problem to differential inclusion form. In [10] the problem is converted to measure space and then solved and in [11] the problem is solved by genetic algorithm, Others deal with the optimal control problem directly. For example see [12][13][14][15][16][17].…”