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

作者：Defterli Ozlem^*

来源：Computers & Mathematics with Applications, 2010, 59(5): 1630-1636.

DOI：10.1016/j.camwa.2009.08.005

• Fractional calculus
• Fractional Hamiltonian
• Variational analysis
• Optimal control
• Quadratic performance indices

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.

• 出版日期2010-3