Abstract In this paper, we focus on the robust partial quadratic eigenvalue assignment problem for vibrating structures by active feedback control. This problem is reformulated as an minimization problem, where the cost function can measure both the sensitivity of the closed-loop eigenvalues and the feedback norms. This can be seen as a modified version of the minimization problem proposed by Bai et al. (2016) [5] , where there exist additional equality constraints involving determinants of linear functions of the parameter matrix. By using the receptance measurements, the system matrices and a few undesired open-loop eigenvalues and associated eigenvectors, we propose a modified gradient-based optimization method for solving the minimization problem, where the explicit gradient formula of the cost function is derived. To implement our method in real operation, the real form of our method is also presented. Finally, some numerical examples are given to illustrate the validity of the proposed method.

中文翻译：

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一种使用接受度和系统矩阵的鲁棒部分二次特征值分配的改进优化方法

摘要 在本文中，我们重点研究了通过主动反馈控制的振动结构的鲁棒部分二次特征值分配问题。这个问题被重新表述为一个最小化问题，其中成本函数可以测量闭环特征值和反馈范数的敏感性。这可以看作是 Bai 等人提出的最小化问题的修改版本。(2016) [5] ，其中存在额外的等式约束，涉及参数矩阵的线性函数的行列式。通过使用接收测量、系统矩阵和一些不需要的开环特征值和相关特征向量，我们提出了一种用于解决最小化问题的改进的基于梯度的优化方法，其中导出了成本函数的显式梯度公式。为了在实际操作中实现我们的方法，还介绍了我们方法的真实形式。最后，给出了一些数值例子来说明所提出方法的有效性。