变系数微分Riccati方程的保辛摄动近似求解

Numerical solution of differential Riccati equation with variable coefficients via symplectic conservative perturbation method

区段混合能方法将微分Riccati方程的求解转化为区段混合能矩阵的计算．针对变系数情形,提出了保辛摄动方法．通过正则变换,将原时变系统分解为零阶和摄动两个Hamilton系统,而零阶系统的混合能矩阵可采用精细积分法精确求解．该方法具有极大的并行性．高效而稳定．算例验证了算法的有效性．同时还讨论了区段混合能方法与改进的Davison-Maki方法之间的关系．

By introducing the concept of interval mixed energy, the key to solve differential Riccati equation is transformed into integrating matrices of interval mixed energy efficiently. For the time-dependent case, a symplectic conservative perturbation method was presented. The original time-varying system was decomposed into two Hamiltonian systems, i. e. a zero-order system and a perturbation system, while the former one could be solved exactly by precise integration method. The proposed method can be implemented with parallel arithmetic. And its effectiveness is verified by two examples. The relations between the interval mixed energy method and the modified Davison-Maki method were also investigated.