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.
Highlights
The control of multi-agent systems has been an active research topic in the systems and control field
We show that consensus by typical controllers can be considered as the spatial lowpass filtering of agent states, which demonstrates that a spatial frequency-based approach is available for multi-agent systems
ANALYSIS OF MULTI-AGENT SYSTEMS IN SPATIAL FREQUENCY DOMAIN: CASE OF CONSENSUS we focus on consensus, which is fundamental to multi-agent systems, and analyze it from the viewpoint of spatial frequencies using graph signal processing techniques
Summary
The control of multi-agent systems has been an active research topic in the systems and control field. Liu et al [24] proposed a robust formation control method for a group of nonlinear and underactuated quadrotors subject to external disturbances These studies, did not consider spatial frequencies for multi-agent systems. This study is based on our preliminary results [25] presented at a conference, but provides the following novel contributions: (i) this study focuses on the spatial frequencybased analysis and design of multi-agent systems as an VOLUME 8, 2020. Extension of [25] where graph signal processing was only applied to multi-agent control; (ii) this paper provides complete explanations and rigorous proofs of the main results, omitted in [25]; (iii) we present a controller design method in the spatial frequency domain; (iv) to demonstrate the effectiveness and applicability of our design method, we show its application to distributed spatial filtering in a sensor network. (L2) If the graph is connected, L has only one zero eigenvalue
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