A numerical scheme for two-dimensional optimal control problems with memory effect

Authors:
Ozlem Defterli
Affiliations:
Çankaya University, Department of Mathematics & Computer Science, Ogretmenler Cad. 14, 06530, Balgat, Ankara, Turkey
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 4
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Abstract

A new formulation for multi-dimensional fractional optimal control problems is presented in this article. The fractional derivatives which are coming from the formulation of the problem are defined in the Riemann-Liouville sense. Some terminal conditions are imposed on the state and control variables whose dimensions need not be the same. A numerical scheme is described by using the Grunwald-Letnikov definition to approximate the Riemann-Liouville Fractional Derivatives. The set of fractional differential equations, which are obtained after the discretization of the time domain, are solved within the Grunwald-Letnikov approximation to obtain the state and the control variable numerically. A two-dimensional fractional optimal control problem is studied as an example to demonstrate the performance of the scheme.