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 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.