Identifying Nonlinear 1-Step Causal Influences in Presence of Latent Variables

We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the causal relations among the observed variables as long as the latent variables evolve without exogenous noise. We further propose an efficient learning method based on linear regression for the special sub-case when the dynamics are restricted to be linear. We validate the performance of our approach via numerical simulations

Learning Exact Topology of a Loopy Power Grid from Ambient Dynamics

Estimation of the operational topology of the power grid is necessary for optimal market settlement and reliable dynamic operation of the grid. This paper presents a novel framework for topology estimation for general power grids (loopy or radial) using time-series measurements of nodal voltage phase angles that arise from the swing dynamics. Our learning framework utilizes multivariate Wiener filtering to unravel the interaction between fluctuations in voltage angles at different nodes and identifies operational edges by considering the phase response of the elements of the multivariate Wiener filter. The performance of our learning framework is demonstrated through simulations on standard IEEE test cases.Comment: accepted as a short paper in ACM eEnergy 2017, Hong Kon

Reconstruction of Directed Networks from Consensus Dynamics

This paper addresses the problem of identifying the topology of an unknown, weighted, directed network running a consensus dynamics. We propose a methodology to reconstruct the network topology from the dynamic response when the system is stimulated by a wide-sense stationary noise of unknown power spectral density. The method is based on a node-knockout, or grounding, procedure wherein the grounded node broadcasts zero without being eliminated from the network. In this direction, we measure the empirical cross-power spectral densities of the outputs between every pair of nodes for both grounded and ungrounded consensus to reconstruct the unknown topology of the network. We also establish that in the special cases of undirected or purely unidirectional networks, the reconstruction does not need grounding. Finally, we extend our results to the case of a directed network assuming a general dynamics, and prove that the developed method can detect edges and their direction.Comment: 6 page

Generalized synchronization-based partial topology identification of complex networks

summary:In this paper, partial topology identification of complex networks is investigated based on synchronization method. We construct the response networks consisting of nodes with sim-pler dynamics than that in the drive networks. By constructing Lyapunov function, sufficient conditions are derived to guarantee partial topology identification by designing suitable controllers and parameters update laws. Several numerical examples are provided to illustrate the effectiveness of the theoretical results