Space-Time Sampling for Network Observability
For control and estimation in networked systems, this work provides a theoretical framework and practical algorithms to reduce sampling requirements while maintaining observability, making network design more cost-effective and resilient.
This paper addresses the problem of designing sparse sampling strategies for estimating the initial condition of linear time-invariant networks from noisy measurements. It reformulates observability as a frame condition and develops three scalable algorithms for space-time sampling with explicit error bounds, showing that coarse samples can retain the same information as finer ones.
Designing sparse sampling strategies is one of the important components in having resilient estimation and control in networked systems as they make network design problems more cost-effective due to their reduced sampling requirements and less fragile to where and when samples are collected. It is shown that under what conditions taking coarse samples from a network will contain the same amount of information as a more finer set of samples. Our goal is to estimate initial condition of linear time-invariant networks using a set of noisy measurements. The observability condition is reformulated as the frame condition, where one can easily trace location and time stamps of each sample. We compare estimation quality of various sampling strategies using estimation measures, which depend on spectrum of the corresponding frame operators. Using properties of the minimal polynomial of the state matrix, deterministic and randomized methods are suggested to construct observability frames. Intrinsic tradeoffs assert that collecting samples from fewer subsystems dictates taking more samples (in average) per subsystem. Three scalable algorithms are developed to generate sparse space-time sampling strategies with explicit error bounds.