LQG量测反馈最优控制的精细积分

对于线性二次型高斯（LQG）量测反馈最优控制问题，提出了精细积分解法。根据分离性原理，LQG控制问题可以分成为最优状态反馈控制问题以及最优状态估计问题，即：离线计算的两套黎卡提微分方程的求解以及状态向量的时变微方程的在线积分解。该算法不仅适用于求解二点边值问题及其相应的黎卡提微分方程，也适用于求解状态估计的时变微分方程。精细积分高精度的特点，对控制和估计都是有利的。数值算例表明了算法的高精度及有效性。

Precise Integration Method for LQG Optimal Measurement Feedback Control Problem

By using the precise integration method, the numerical solution of linear quadratic Gaussian (LQG) optimal control problem was discussed. Based on the separation principle, the LQG control problem decomposes, or separates, into an optimal state_feedback control problem and an optimal state estimation problem. That is the off_line solution of two sets of Riccati differential equations and the on_line integration solution of the state vector from a set of time_variant differential equations. The present algorithms are not only appropriate to solve the two_point boundary_value problem and the corresponding Riccati differential equation, but also can be used to solve the estimated state from the time_variant differential equations. The high precision of precise integration is of advantage for the control and estimation. Numerical examples demonstrate the high precision and effectiveness of the algorithm.