线性时变系统二次最优控制问题的保辛近似求解

状态空间的最优控制体系是保守的，其近似算法应当保辛．提出了基于分段常值精细积分方法的保辛摄动近似方法，在同一框架下求解了线性时变LQ最优控制中的计算问题，即变系数矩阵Riccati方程和状态反馈方程．该算法是保辛的，具有很好的数值稳定性和精度．算例验证了算法的有效性．

Numerical Solutions of LQ Control for Time-Varying Systems Via Symplectic Conservative Perturbation

Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation was presented. It gives a uniform way to solve the LQ control problems for linear time-varying systems accurately and efficiently, whose key points are solutions of differential Riccati equation and the state feedback equation with variable coefficient. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed method.