Numerical optimal unbounded control with a singular integro-differential equation as a constraint

Pages: 129 - 137, Issue special, November 2013

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Shihchung Chiang - Department of Applied Statistics, Chung Hua University, Hsinchu, Taiwan (email)

Abstract: This study presents a discussion of numerical methods for optimal control using an integro-differential equation of singular kernel as a constraint. The proposed scheme attempts to set the objective to minimize the gap between optimal state and target function for certain period of time. By assuming that control is unbounded, this study proposes a method of feedback correction that makes correction each step for optimal control. These corrections are proportional to the corresponding state-target distance until a certain accuracy criterion is satisfied. There are several advantages to this method, including user-decided accuracy, user-decided number of iterations, and time saving. This study presents a comparison of the numerical results with the results of other methods [4],[7].

Keywords:  Integro-differential equations, objective function, optimal control, optimal state.
Mathematics Subject Classification:  Primary: 34K28, 49J30; Secondary: 45E10.

Received: August 2012;      Revised: March 2013;      Published: November 2013.