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

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 transformedinto a non-linear two-point boundary value problem by using the Pontryaginsmaximum principle (PMP). Then, we applied the q-HAM to solve this system. Theproposed method is based on the HAM but the q-HAM, has an increased intervalof convergence than the HAM. Three examples are provided to demonstrate the reliabilityand efficiency of the method. Next, the numerical results of the proposedmethod 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 othermethods.

Keywords:

q- homotopy analysis method , Non-linear optimal control problems , Pontryagins maximum principle , Analytic - approximate solution