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.