State estimation and sensor selection problems for nonlinear networks and systems are ubiquitous problems that are important for the control, monitoring, analysis, and prediction of a large number of engineered and physical systems. Sensor selection problems are extensively studied for linear networks. However, less attention has been dedicated to networks with nonlinear dynamics. Furthermore, widely used sensor selection methods relying on structural (graph-based) observability approaches might produce far from optimal results when applied to nonlinear network dynamics. In addition, state estimation and sensor selection problems are often treated separately, and this might decrease the overall estimation performance. To address these challenges, we develop a novel methodology for selecting sensor nodes for networks with nonlinear dynamics. Our main idea is to incorporate the sensor selection problem into an initial state estimation problem. The resulting mixed-integer nonlinear optimization problem is approximately solved using three methods. The good numerical performance of our approach is demonstrated by testing the algorithms on prototypical Duffing oscillator, associative memory, and chemical reaction networks. The developed codes are available online.

中文翻译：

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非线性网络和系统的联合传感器节点选择和状态估计

非线性网络和系统的状态估计和传感器选择问题是普遍存在的问题，对于大量工程和物理系统的控制、监测、分析和预测都很重要。传感器选择问题被广泛研究用于线性网络。然而，很少有人关注具有非线性动力学的网络。此外，广泛使用的依赖于结构（基于图）可观察性方法的传感器选择方法在应用于非线性网络动力学时可能会产生远非最佳结果。此外，状态估计和传感器选择问题通常被分开处理，这可能会降低整体估计性能。为了应对这些挑战，我们开发了一种为具有非线性动力学的网络选择传感器节点的新方法。我们的主要思想是将传感器选择问题合并到初始状态估计问题中。由此产生的混合整数非线性优化问题使用三种方法近似求解。通过在原型 Duffing 振荡器、联想记忆和化学反应网络上测试算法，证明了我们方法的良好数值性能。开发的代码可在线获得。