Proceedings of the Conference on Nonlinear Coherent Structures in Physics and Biology, Heriot-Watt University, Edinburgh, July 95

Global Control of a Nonlinear Wave Equation

M. H. Farahi

Department of Applied Mathematical Studies,
Leeds University, Leeds, U.K.

Abstract

We consider the existence and numerical estimation of the distributed control of a nonlinear wave equation with an integral performance criterion and fixed final state. The problem is modified into one consisting of the minimization of a linear form over a set of pairs of positive measures satisfying linear constrains. The minimizer in the new problem is global; it can be approximated by means of the solution of a finite-dimensional linear programming problem. The solution of this problem is used to construct a nearly optimal control. An example is given to illustrate the procedure.