Particle filtering of dynamical networks: Highlighting observability issues

Abstract

In a network of high-dimensionality, it is not feasible to measure every single node. Thus, an important goal in the literature is to define the optimal choice of sensor nodes that provides a reliable state reconstruction of the network system state-space. This is an observability problem. In this paper, we propose a particle filtering (PF) framework as a way to assess observability properties of a dynamical network, where each node is composed by an individual dynamical system. The PF framework is applied on two benchmarks, networks of Kuramoto and Rössler oscillators, to investigate how the interplay between dynamics and topology impacts the network observability. Based on the numerical results, we conjecture that, when the network nodal dynamics are heterogeneous, better observability is conveyed for sets of sensor nodes that share some dynamical affinity to its neighbourhood. Moreover, we also investigate how the choice of an internal measured variable of a multidimensional sensor node affects the PF performance. The PF framework effectiveness as an observability measure is compared to a well-consolidated nonlinear observability metric for a small network case and some chaotic systems benchmarks.

Functional observability and subspace reconstruction in nonlinear systems

“…1a-c shows that unobservable regions hamper the quality of the attractor reconstruction from an embedded time series. Consequently, the applicability and performance of methods based on embedding [23][24][25] and state estimation [26][27][28] are highly dependent on the observability properties of the system. Building from chaotic systems, often used as benchmark cases due to their short horizon of predictability, observability studies showed the potential to foster further discoveries in complex systems, (c) Reconstruction of the original coordinates of the Lorenz system from the differential embedding.…”

Functional observability and target state estimation in large-scale networks

“…However, even if a minimum set of sensors is used, the state observer will have the same dimension as the entire network, making its design and implementation computationally expensive in large-scale systems. Moreover, a minimum set of sensor nodes does not guarantee good quality for the full-state reconstruction in higher-order systems [16][17][18][19][20].…”