Optimization
Maryam Alipour; Samaneh Soradi zeid
Abstract
This paper deals with a general form of fractional optimal control problems involving variable-order fractional integro differential equation using orthonormal Laguerre wavelets expansions. By effectively employing these functions, product variable-order operational matrices have been ...
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This paper deals with a general form of fractional optimal control problems involving variable-order fractional integro differential equation using orthonormal Laguerre wavelets expansions. By effectively employing these functions, product variable-order operational matrices have been obtained. By using these fractional operational matrices and collocation points, the study transforms the original continuous-time optimal control problems of variable-order fractional integro-differential equations into a system of linear or non-linear algebraic equations. Attempts have been made to use the collocation method with a joint application of Lagrange multiplier technique, to obtain the approximate cost function based on determining the state and control functions. The main components for applying these wavelets is to have viable solutions due to their orthogonality. In addition, the convergence analysis is presented with respect to the operational matrices of this scheme. Simulation results indicate that the proposed method works well and provides satisfactory results with regard to accuracy and computational effort.
Control
fahimeh akhavan ghassabzadeh; Samaneh Soradi zeid
Abstract
Due to the easy adaption of radial basis functions (RBFs), a directRBF collocation method is considered to develop an approximate scheme to solvefractional delay differential equations (FDDEs). The method of RBFs is a method of scattered data interpolation that has many application in different fields. ...
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Due to the easy adaption of radial basis functions (RBFs), a directRBF collocation method is considered to develop an approximate scheme to solvefractional delay differential equations (FDDEs). The method of RBFs is a method of scattered data interpolation that has many application in different fields. In spite of easy implementation of other high-order methods and finite difference schemes for solving a problem of fractional order derivatives, the challenge of these methods is their limited accuracy, locality, complexity and high cost of computing in discretization of the fractional terms, which suggest that global scheme such as RBFs that are more accurate way for discretizing fractional calculus and would allow us to remove the ill-conditioning of the system of discrete equations. Applications to a variety ofproblems confirm that the proposed method is slightly more efficient than thoseintroduced in other literature and the convergence rate of our approach is high.
