
Journal of the Australian Mathematical Society  Series B
Vol. 40 Part 2 (1998)
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
secondorder 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.
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