  This paper presents a new method for solving a class of nonlinear optimal
control problems with a quadratic performance index. In this method, first the
original optimal control problem is transformed into a nonlinear two-point
boundary value problem (TPBVP) via the Pontryagin's maximum principle. Then,
using the Homotopy Perturbation Method (HPM) and introducing a convex homotopy
in topologic space, the nonlinear TPBVP is transformed into a sequence of
linear time-invariant TPBVP's. By solving the presented linear TPBVP sequence
in a recursive manner, the optimal control law and the optimal trajectory are
determined in the form of infinite series. Finally, in order to obtain an
accurate enough sub-optimal control law, an iterative algorithm with low
computational complexity is introduced. An illustrative example demonstrates
the simplicity and efficiency of proposed method.
