To obtain a control function which puts the wave equation in an unknown minimum time into a stationary regime is considered is considered. Using an embedding method, the problem of ¯nding the time optimal control is reduced to one consisting of minimizing a linear form over a set of positive measures. The resulting problem can be approximated by a finite dimensional linear programming (LP) problem. The nearly optimal control is constructed from the solution of the final LP problem. To find the lower bound of the optimal time a search algorithm is proposed. Some examples demonstrate the e®ectiveness of the method.

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