An Approach for Simultaneously Determining the Optimal Trajectory and Control of a Vibrating Shell

Abstract

In this article, for a two-dimensional wave control system, we are going to present a new combinational solution path. First, by considering all necessary conditions, the problem is represented in a variational format in which the trajectory is shown by a trigonometric series with the unknown coefficients. Then the problem is converted into a new one that the unknowns are the mentioned coefficients and a positive Radon measure. It is proved that the optimal solution is existed and it is also explained how the optimal pair would be identified from the results deduced by a finite linear programming problem simultaneously. Two numerical examples are also given.

Key words and phrases. Vibrating Shell, Optimal control, trigonometric series, Measure, Linear programing.

2000 Mathematics Subject Classification. 49QJ20, 49J45, 49M25, 76D33