Analysis and Design of Multi-Agent Systems in Spatial Frequency Domain: Application to Distributed Spatial Filtering in Sensor Networks

Abstract

This study attempts to analyze and design multi-agent systems in the spatial frequency domain and demonstrates that the spatial frequency-based approach is useful for distributed spatial filtering in sensor networks. First, we take the consensus of multi-agent systems (i.e., letting the states of all agents converge to an identical value) as an example and analyze it using the concept of spatial frequencies. We then show that consensus by typical controllers corresponds to lowpass filtering in the spatial frequency domain. This demonstrates that spatial frequencies can characterize the behavior of multi-agent systems. Second, we present a controller design method in the spatial frequency domain. The designed controllers provide the feedback system with a desired spatial frequency characteristic given in advance. We further derive a sufficient condition for the spatial frequency characteristic to ensure that the designed controllers are distributed. Finally, the effectiveness and applicability of our design method are demonstrated through an example of distributed denoising in a sensor network. INDEX TERMS Distributed control, graph signal processing, multi-agent systems, sensor networks, spatial frequency domain.

Distributed Spatial Filtering Over Networked Systems

“…Motivated by this, Izumi et al [9] proposed a method of DSF based on a consensus algorithm. However, the following two issues remain unsolved.…”

“…Overcoming this issue broadens the application range of DSF. Second, the method proposed in [9] was not verified through experiments. DSF requires wireless communications between nodes, but they are unreliable in practice, which leads to gaps between theory and practice.…”

“…(i) We extend the theoretical framework developed in [9]. By introducing a new design parameter, we extend the filtering algorithm given in [9].…”

“…(i) We extend the theoretical framework developed in [9]. By introducing a new design parameter, we extend the filtering algorithm given in [9]. We then characterize all the achievable filter characteristics for the extended algorithm, unlike in [9], where all the achievable filter characteristics were not guaranteed to be characterized.…”

“…By introducing a new design parameter, we extend the filtering algorithm given in [9]. We then characterize all the achievable filter characteristics for the extended algorithm, unlike in [9], where all the achievable filter characteristics were not guaranteed to be characterized. The result shows that the extended algorithm provides a wide range of filter characteristics compared to the original algorithm, and further reveals its performance limit as the spatial filter.…”