This study proposes a method for the static output feedback (SOF) stabilization of discrete time linear time invariant (LTI) systems by using a low number of sensors. The problem is investigated in two parts. First, the optimal sensor placement is formulated as a quadratic mixed integer problem that minimizes the required input energy to steer the output to a desired value. Then, the SOF stabilization, which is one of the most fundamental problems in the control research, is investigated. The SOF gain is calculated as a projected solution of the Hamilton-Jacobi-Bellman (HJB) equation for discrete time LTI system. The proposed method is compared with several examples from the literature.

中文翻译：

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基于近似动态规划的离散时间线性时不变系统静态输出反馈镇定

本研究提出了一种通过使用少量传感器来稳定离散时间线性时不变 (LTI) 系统的静态输出反馈 (SOF) 的方法。该问题分两部分进行研究。首先，最佳传感器放置被公式化为二次混合整数问题，该问题最小化所需的输入能量以将输出引导至所需值。然后，对控制研究中最基本的问题之一的 SOF 稳定性进行了研究。SOF 增益计算为离散时间 LTI 系统的 Hamilton-Jacobi-Bellman (HJB) 方程的投影解。所提出的方法与文献中的几个例子进行了比较。