Haber Aleksandar, Molnar Ferenc, Motter Adilson E
Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208 USA, when this research was performed. He is now with the Department of Engineering Science and Physics, City University of New York, College of Staten Island, Staten Island, NY 10314 USA.
Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208 USA.
IEEE Trans Control Netw Syst. 2018 Jun;5(2):694-708. doi: 10.1109/TCNS.2017.2728201. Epub 2017 Jul 17.
A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system. However, network states are usually unknown, and only a fraction of the state variables are directly measurable. The observability problem concerns reconstructing the network state from this limited information. Here, we propose a general optimization-based approach for observing the states of nonlinear networks and for optimally selecting the observed variables. Our results reveal several fundamental limitations in network observability, such as the trade-off between the fraction of observed variables and the observation length on one side, and the estimation error on the other side. We also show that, owing to the crucial role played by the dynamics, purely graph-theoretic observability approaches cannot provide conclusions about one's practical ability to estimate the states. We demonstrate the effectiveness of our methods by finding the key components in biological and combustion reaction networks from which we determine the full system state. Our results can lead to the design of novel sensing principles that can greatly advance prediction and control of the dynamics of such networks.
各种各样的动力系统，如化学和生物分子系统，都可被视为非线性实体的网络。对此类非线性网络的预测、控制和识别需要了解系统的状态。然而，网络状态通常是未知的，只有一小部分状态变量可直接测量。可观测性问题涉及从这些有限信息中重建网络状态。在此，我们提出一种基于优化的通用方法，用于观测非线性网络的状态并最优地选择观测变量。我们的结果揭示了网络可观测性中的几个基本限制，比如一方面是观测变量的比例与观测长度之间的权衡，另一方面是估计误差。我们还表明，由于动力学所起的关键作用，纯粹的图论可观测性方法无法就估计状态的实际能力得出结论。我们通过找出生物和燃烧反应网络中的关键组件来确定整个系统状态，从而证明了我们方法的有效性。我们的结果可促成新型传感原理的设计，这能极大地推动对此类网络动力学的预测和控制。
