摘要
LQ控制虽然是最优控制的最基本问题 ,但其数值求解仍有很多问题 .黎卡提微分方程的精细积分法利用黎卡提方程的解析特点 ,求出计算机上高度精密的解 ,并已证明误差在计算机倍精度数的误差范围之外 .这对于 Kalman- Bucy滤波 ,LQG问题以及 H∞ 控制及滤波等都可运用 ,精细积分还求解了反馈后的状态微分方程 .数例验证了其高精度特性 .
Linear quadratic control is one of the basic problems for optimal control, however, its numerical computations still have to be solved. The precise integration of the Riccati matrix differential equations introduced in this paper is very attractive. The analytic characteristics of the Riccati equation is applied to deriving the high precision numerical solution so that the full computer precision is reached. The same method can also be applied to such as Kalman-Bucy filtering, LQG and H ∞ control problems. The precise integration method differs from the usual finite difference style method dramatically, and the numerical examples verify the high precision of the solutions. The state vector equation under optimal control is also solved by the precise integration method.
出处
《自动化学报》
EI
CSCD
北大核心
2001年第2期166-173,共8页
Acta Automatica Sinica
