  This paper presents a new and straightforward procedure for solving bilinear
quadratic optimal control problem. In this method, first the original optimal
control problem is transformed into a nonlinear twopoint boundary value problem
(TPBVP) via the Pontryagin's maximum principle. Then, the nonlinear TPBVP is
transformed into a sequence of linear time-invariant TPBVPs using the homotopy
perturbation method (HPM) and introducing a convex homotopy in topologic space.
Solving the latter problems through an iterative process yields the optimal
control law and optimal trajectory in the form of infinite series. Finally,
sufficient condition for convergence of these series is proved by a theorem.
Simplicity and efficiency of the proposed method is shown through an
illustrative example.
