Extraction of Approximate Solution for a Class of‎ ‎Nonlinear Optimal Control Problems Using 1/G'-Expansion Technique

Document Type : Research Article


1 Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran.

2 Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran

3 Department of Applied Mathematics‎, ‎University of Science and Technology of Mazandaran‎, ‎Behshahr‎, ‎Iran‎


In this paper‎, ‎the benefits of 1/G'-expansion technique are utilized to create a direct scheme for extracting approximate solutions for a class of optimal control problems‎. ‎In the given approach‎, ‎first state and control functions have been parameterized as a power series‎, ‎which is constructed according to the solutions of a Bernoulli differential equation‎, ‎where the number of terms in produced power series is determined by the balance method‎. ‎A proportionate replacement and solving the created optimization problem lead to suitable solutions close to the analytical ones for the main problem‎. ‎Numerical experiments are given to evaluate the quality of the proposed method.


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