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On infinite-horizon optimal control problems. (English) Zbl 0964.49003

Summary: We consider infinite-horizon optimal control problems. First, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measure. The optimal measure is approximated by a finite combination of atomic measures and the approximate solution of the first problem is found by the optimal solution of a finite-dimensional linear programming problem. The solution of this problem is used to find a piecewise constant control for the original one, and finally by using the approximate control signals we obtain the approximate trajectories.

MSC:

49J15 Existence theories for optimal control problems involving ordinary differential equations
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References:

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