论文标题
基于系统平衡的哈米尔顿港模型和控制器减少控制器的错误界限
Error bounds for port-Hamiltonian model and controller reduction based on system balancing
论文作者
论文摘要
我们研究线性端口 - 哈米尔顿系统的线性二次高斯（LQG）控制设计。为此，我们利用了选择加权矩阵的自由，并提出了一种特定的选择，该选择导致了LQG控制器，该控制器是哈米尔顿港，因此特别是稳定和被动的。此外，我们通过平衡和随后的截断来构建一个减少订单控制器。这种方法与经典的LQG平衡截断密切相关，并且相对于GAP度量，共享类似的先验误差。通过利用哈密顿量的非唯一性，我们能够确定全阶系统的最佳pH表示，从而使误差结合的意义最小化。此外，我们讨论了pH保护平衡截断模型还原的后果，这导致了两种不同的经典H-内率界限。最后，我们通过两个数值示例来说明理论发现。
We study linear quadratic Gaussian (LQG) control design for linear port-Hamiltonian systems. To this end, we exploit the freedom in choosing the weighting matrices and propose a specific choice which leads to an LQG controller which is port-Hamiltonian and, thus, in particular stable and passive. Furthermore, we construct a reduced-order controller via balancing and subsequent truncation. This approach is closely related to classical LQG balanced truncation and shares a similar a priori error bound with respect to the gap metric. By exploiting the non-uniqueness of the Hamiltonian, we are able to determine an optimal pH representation of the full-order system in the sense that the error bound is minimized. In addition, we discuss consequences for pH-preserving balanced truncation model reduction which results in two different classical H-infinity-error bounds. Finally, we illustrate the theoretical findings by means of two numerical examples.
