Sendiña-Nadal Irene, Letellier Christophe
Complex Systems Group & GISC, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.
Rouen Normandie Université-CORIA, Campus Universitaire du Madrillet, F-76800 Saint-Etienne du Rouvray, France.
Chaos. 2022 Aug;32(8):083109. doi: 10.1063/5.0090239.
We address the problem of retrieving the full state of a network of Rössler systems from the knowledge of the actual state of a limited set of nodes. The selection of nodes where sensors are placed is carried out in a hierarchical way through a procedure based on graphical and symbolic observability approaches applied to pairs of coupled dynamical systems. By using a map directly obtained from governing equations, we design a nonlinear network reconstructor that is able to unfold the state of non-measured nodes with working accuracy. For sparse networks, the number of sensor scales with half the network size and node reconstruction errors are lower in networks with heterogeneous degree distributions. The method performs well even in the presence of parameter mismatch and non-coherent dynamics and for dynamical systems with completely different algebraic structures like the Hindmarsch-Rose; therefore, we expect it to be useful for designing robust network control laws.
我们解决了从有限节点集的实际状态信息中恢复罗塞尔系统网络完整状态的问题。通过基于应用于耦合动力系统对的图形和符号可观测性方法的程序，以分层方式进行放置传感器节点的选择。通过使用直接从控制方程获得的映射，我们设计了一种非线性网络重构器，它能够以工作精度展开未测量节点的状态。对于稀疏网络，传感器数量按网络大小的一半缩放，并且在具有异构度分布的网络中节点重构误差更低。即使存在参数失配和非相干动力学，并且对于具有完全不同代数结构（如 Hindmarsch-Rose）的动力系统，该方法也表现良好；因此，我们期望它对设计鲁棒的网络控制律有用。
