Solution of Dynamic Optimization Problems Constrained by the Fraction Penalty Method

Hartono Hartono


This article discusses the application of fractional penalty method to solve dynamic optimization problem with state constraints. The main theories supporting the use of the method are described in some theorem and corollary. The theorems give sufficient conditons for the application of the method. Therefore, if all conditions mentioned in the theorems are met then the resulted solution will converge to the analytic solution. In addition, there are some examples to support the theory. The numerical simulation shows that the accuracy of the method is quite good. Hence, this method can play a role as an alternative method for solving dynamic optimization problem with state constrints.


dynamic optimization; state constraints; Pontryagin minimum principle; fractional penalty method

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J. A. Snyman, C. Frangos, and Y. Yavin, “Penalty function solutions to optimal control problems with general constraints via a dynamic optimisation method,” Comput. Math. with Appl., 1992.

A. . Xing, “The Exact Penalty Function Method in Constrained Optimal Control Problems,” J. Math. Anal. Appl., 1994.

Q. H.Y, “A Penalty Method for Solving Inequality Path Constrained Optimal Control Problems,” Acta Autom. Sin., 2013.

P. Malisani, F. Chaplais, and N. Petit, “An interior penalty method for optimal control problems with state and input constraints of nonlinear systems,” Optim. Control Appl. Methods, 2016.

J. L. Speyer and D. H. Jacobson, Primer on Optimal Control Theory. 2010.

M. I. Kamien, Dynamic Optimization: The Calculus of Variations and Optimal Control in Economic and Management, 2nd ed. New York: Dover, 2013.

C. J. Goh and K. L. Teo, “Control parametrization: A unified approach to optimal control problems with general constraints,” Automatica, 1988.

L. S. Jennings, MISER 3 Optimal Control Software: Theory and User Manual version 3. Perth: Department of Mathematics, University of Western Australia, 2004.



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