Numerical Solutions of LQ Control for Time-Varying Systems Via Symplectic Conservative Perturbation
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摘要: 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．Abstract: 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.
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