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# Zeitschrift für Analysis und ihre Anwendungen

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**Volume 19, Issue 1, 2000, pp. 269–278**

**DOI: 10.4171/ZAA/950**

Published online: 2000-03-31

On Infinite-Horizon Optimal Control Problems

S. Effati^{[1]}, A.V. Kamyad

^{[2]}and R.A. Kamyabi-Gol

^{[3]}(1) Ferdowsi University, Mashhad, Iran

(2) Ferdowski University, Mashhad, Iran

(3) Ferdowsi University, Mashhad, Iran

In this paper, 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 fist problem is find 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.

*Keywords: *Infinite-horizon problems, measure theory, optimal control, linear programming

Effati S., Kamyad A.V., Kamyabi-Gol R.A.: On Infinite-Horizon Optimal Control Problems. *Z. Anal. Anwend.* 19 (2000), 269-278. doi: 10.4171/ZAA/950