Exploiting Sparsity in Direct Orthogonal Collocation Methods for Solving Multiple-Phase Optimal Control Problems

2018 ◽  
Author(s):  
Yunus M. Agamawi ◽  
Anil V. Rao
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Collocation Methods ◽  
Control Problems ◽  
Orthogonal Collocation ◽  
Multiple Phase ◽  
Direct Orthogonal Collocation

scholarly journals Shifted ultraspherical pseudo-Galerkin method for approximating the solutions of some types of ordinary fractional problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohamed Abdelhakem ◽  
Doha Mahmoud ◽  
Dumitru Baleanu ◽  
Mamdouh El-kady
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problems ◽  
Approximate Solutions ◽  
Collocation Methods ◽  
Control Problems ◽  
Algebraic Equations ◽  
Fractional Optimal Control ◽  
Ultraspherical Polynomials ◽  
Fractional Optimal Control Problems

AbstractIn this work, a technique for finding approximate solutions for ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is a hybrid between Galerkin and collocation methods. Also, this method can be extended to approximate fractional integro-differential equations (FIDEs) and fractional optimal control problems (FOCPs). The spatial approximations with their derivatives are based on shifted ultraspherical polynomials (SUPs). Modified Galerkin spectral method has been used to create direct approximate solutions of linear/nonlinear ordinary fractional differential equations, a system of ordinary fraction differential equations, fractional integro-differential equations, or fractional optimal control problems. The aim is to transform those problems into a system of algebraic equations. That system will be efficiently solved by any solver. Three spaces of collocation nodes have been used through that transformation. Finally, numerical examples show the accuracy and efficiency of the investigated method.

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