A new application of q- homotopy analysis method to solve non-linear optimal control problems

Document Type : Research Articles

Authors

1 Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.

2 Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Abstract

This paper advances a new application of q-homotopy analysis method (q-HAM)
to solve non-linear optimal control problems(NOCPs). First, the NOCP was transformed
into a non-linear two-point boundary value problem by using the Pontryagins
maximum principle (PMP). Then, we applied the q-HAM to solve this system. The
proposed method is based on the HAM but the q-HAM, has an increased interval
of convergence than the HAM. Three examples are provided to demonstrate the reliability
and efficiency of the method. Next, the numerical results of the proposed
method are compared with those of other methods. As can be seen from the tables,
the maximum error in the second and third examples is much better than other
methods.

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