The optimization of the time-invariant bilinear weakly coupled system with a quadratic performance criterion is considered. A sequence of linear state and costate equations is constructed such that the open-loop solution of the optimization problem is obtained in terms of the reduced-order subsystems. This leads to a reduction in the size of the required computations and allows parallel processing of information. The near-optimal closed-loop control is obtained in the form of a linear feedback law, with the feedback gains calculated from two reduced-order independent time-varying linear-quadratic optimal control problems.