A method was developed for deriving the control input for a multi-dimensional discrete-time nonlinear system so that a performance index is approximately minimized. First, a moment vector equation (MVE) is derived; it is a multi-dimensional linear equation that approximates a nonlinear system in the whole domain of the system state and control input. Next, the performance index is approximated by using a quadratic form with respect to the moment vector. On the basis of the MVE and the quadratic form, an approximate optimal controller is derived by solving the linear quadratic optimal control problem. A bilinear optimal control problem and a mountain-car problem were solved using this method, and the solutions were nearly optimal.

We developed a priority queueing method that can keep the loss ratio of high-priority packets at a target value. It regulates the number of input low-priority packets when the queue length exceeds the threshold that is adjusted so as to minimize the Lyapunov function of the system. We showed that the number of calculations for the optimum threshold is sufficiently small and derived a sufficient condition for the proposed method to be robust against unknown load fluctuations. From the viewpoint of guaranteeing the loss ratio of high-priority packets, we showed, by computer simulation and theoretical analysis, that the proposed method is superior to conventional methods such as the fixed-threshold method and the pushout method.