In this paper we consider the Time Optimal Control Problem with Bounded state (TOCPB). By means of a process of embedding and using measure theory, this problem is replaced by another, in which we seek to minimize a linear form over a subset of a measure space defined by linear equalities. The theory allows us to convert the new problem to an infinite-dimensional linear programming problem. Afterwards, the infinite-dimensional linear programming problem is approximated by a finite dimensional one. Then by the solution of the final linear programming problem one can find an approximate value of the trajectory function , control function and optimal time T as well.
AMS classification(49A).
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