Numerical Method for Solving Optimal Control Problem of Stochastic Volterra Integral Equations Using Block Pulse Functions

Volume 11, Issue 1, pp 22-36 http://dx.doi.org/10.22436/jmcs.011.01.03

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Authors

M. Saffarzadeh - Department of Mathematics, Yazd University P.O. Box: 89195-741 Yazd, Iran. A. Delavarkhalafi - Department of Mathematics, Yazd University P.O. Box: 89195-741 Yazd, Iran. Z. Nikoueinezhad - Department of Mathematics, Yazd University P.O. Box: 89195-741 Yazd, Iran.

Abstract

In this paper, a numerical method for solving a general optimal control of systems is presented. These systems governed by stochastic Volterra integral equations. This method is based on block pulse functions. By using the properties of block pulse functions and associated operational matrices, optimal control problem is converted to an optimization problem and will be solved via mathematical programming techniques. The error estimations and associated theorems have been provided. Finally, some numerical examples are presented to show the validity and efficiency of the proposed method.

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Keywords

• Stochastic Volterra integral equations
• Optimal control
• Block pulse functions
• Stochastic operational matrix.

MSC

•  65R20
•  49J15
•  45D05

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