Computing optimal control with a hyperbolic partial differential equation

V. Rehbock
School of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth, 6845, Australia
and
S. Wang
School of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth, 6845, Australia
and
K. L. Teo
School of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth, 6845, Australia

Abstract:

We present a method for solving a class of optimal control problems involving hyperbolic partial differential equations. A numerical integration method for the solution of a general linear second-order hyperbolic partial differential equation representing the type of dynamics under consideration is given. The method, based on the piecewise bilinear finite element approximation on a rectangular mesh, is explicit. The optimal control problem is thus discretized and reduced to an ordinary optimization problem. Fast automatic differentiation is applied to calculate the exact gradient of the discretized problem so that existing optimization algorithms may be applied. Various types of constraints may be imposed on the problem. A practical application arising from the process of gas absorption is solved using the proposed method.