ANALYTIC-APPROXIMATE SOLUTION FOR A CLASS OF NONLINEAR OPTIMAL CONTROL PROBLEMS BY HOMOTOPY ANALYSIS METHOD

In this paper, we apply the homotopy analysis method (HAM) for nonlinear quadratic optimal control problems (OCP's). This method is employed to solve extreme conditions obtained from the Pontryagin's maximum principle (PMP). Applying the HAM, we in essence transfer a nonlinear two-point boundary value problem (TPBVP), into an infinite number of linear sub-problems, and then use the sum of the solutions of its first several sub-problems to approximate the exact solution. Note that such a kind of transformation does not need the existence of any small or large parameters in governing equation and initial/boundary conditions. The comparison of the HAM results with the Measure theory method, Modal series and collocation method solutions are made. Some illustrative examples are given to demonstrate the simplicity and efficiency of the proposed method.