This article proposes a method that combines linear quadratic Gaussian (LQG) control design and structure preserving model reduction for the reduced order control of infinite dimensional port Hamiltonian systems (IDPHS).For that purpose the weighting operators used in LQG control design are chosen such that the resulting dynamic controller is passive and the closed-loop system equivalent to control by interconnection. The method of Petrov-Galerkin is then used to approximate the balanced realization of the IDPHS by a finite dimensional port Hamiltonian system and to provide the associated reduced order LQG controller. The main advantages of the proposed method are that, first, both control and reduction are driven by closed-loop performances and that, second, due to the passivity properties of the controller the closed-loop stability is guaranteed when the finite dimensional controller is applied to the infinite dimensional system.

中文翻译：

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无限维端口哈密顿系统的降阶LQG控制设计


本文提出了一种结合线性二次高斯 (LQG) 控制设计和结构保持模型简化的方法，用于无限维端口哈密顿系统 (IDPHS) 的降阶控制。为此，选择 LQG 控制设计中使用的加权算子，使得由此产生的动态控制器是无源的，闭环系统相当于互连控制。然后使用 Petrov-Galerkin 方法通过有限维端口哈密顿系统来近似 IDPHS 的平衡实现，并提供相关的降阶 LQG 控制器。该方法的主要优点是，首先，控制和缩减都是由闭环性能驱动的，其次，由于控制器的无源特性，当应用有限维控制器时，保证了闭环稳定性到无限维系统。