状态空间对称系统的L2最优模型降价

研究用一个低价隐定连续线对称性时不变系统上近似一个高阶隐定连续线对称性时不变系统以使它们之间的L2-范数误差最小化，到目前为止，这一问题是否有解还没有定论。该文试图寻找一个低阶隐定连续线对称性时不变系统，其与给定的高阶隐定连续线对称性时不变系统的L2-范数误差可与最优误差值充分接近。为此，构造一个约束最小化问题并证明这个问题有全局最小解，作者设计一个梯度流算法来求解这个约束最小化问题，给出一个数值例子显示本方法的有效性。

L2Optimal Model Reduction for State Space Symmetrc

This paper deals with the problem of finding a lower-order linear continuous time-invariant stable state space symmetric system to approximate a given higher-order linear continuous time-invariant stable state space symmetric system so that the L_2 norm of the model mismatch is minimized. It is still an open problem whether this problem has a solution or not. This paper attempts to find a lower-order state space symmetric model whose model reduction cost differs from the optimal model reduction cost by a prescribed precision. It is shown that this task can be tackled by solving a smooth constrained optimization problem which is guaranteed to admit a global minimum. A gradient flow algorithm is proposed to solve the latter problem. A numerical example is presented to demonstrate the effectiveness of this approach.