In this article, we consider the optimal design of networked estimators to minimize the communication/measurement cost under the networked observability constraint. This problem is known as the minimum-cost networked estimation problem, which is generally claimed to be NP-hard. The main contribution of this work is to provide a polynomial-order solution for this problem under the constraint that the underlying dynamical system is self-damped. Using structural analysis, we subdivide the main problem into two NP-hard subproblems known as (i) optimal sensor selection, and (ii) minimum-cost communication network. For self-damped dynamical systems, we provide a polynomial-order solution for subproblem (i). Further, we show that the subproblem (ii) is of polynomial-order complexity if the links in the communication network are bidirectional. We provide an illustrative example to explain the methodologies.

中文翻译：

---

自阻尼动力系统最小代价网络估计的复杂性

在本文中，我们考虑了网络估计器的优化设计，以在网络可观察性约束下最小化通信/测量成本。这个问题被称为最小成本网络估计问题，它通常被称为 NP-hard。这项工作的主要贡献是在底层动力系统是自阻尼的约束下为这个问题提供多项式阶解决方案。使用结构分析，我们将主要问题细分为两个 NP 难子问题，称为 (i) 最佳传感器选择和 (ii) 成本最低的通信网络。对于自阻尼动力系统，我们为子问题 (i) 提供多项式阶解决方案。此外，我们表明，如果通信网络中的链路是双向的，子问题 (ii) 具有多项式阶复杂度。