Multi-Partite Output Regulation of Multi-Agent Systems
For researchers in multi-agent systems, this work generalizes existing output regulation problems to arbitrary partitions, but the contribution is incremental as it builds on known cooperative and bipartite frameworks.
This paper introduces the multi-partite output regulation problem (MORP) for heterogeneous linear multi-agent systems, which generalizes cooperative and bipartite output regulation. The authors propose two distributed control design strategies, with the second being more scalable under a mild structural condition, and demonstrate the approach through experiments and numerical examples.
This article proposes a simple, graph-independent perspective on partitioning the node set of a graph and provides multi-agent systems (MASs) with objectives beyond cooperation and bipartition. Specifically, we first introduce the notion of $k$-partition transformation to achieve any desired partition of the nodes. Then, we use this notion to formulate the multi-partite output regulation problem (MORP) of heterogeneous linear MASs, which comprises the existing cooperative output regulation problem (CORP) and bipartite output regulation problem (BORP) as subcases. The goal of the MORP is to design a distributed control law such that each follower that belongs to the same set in the partition asymptotically tracks a scalar multiple of the reference while ensuring the internal stability of the closed-loop system. It is shown that the necessary and sufficient conditions for the solvability of the MORP with a feedforward-based distributed control law follow from the CORP and lead to the first design strategy for the control parameters. However, it has a drawback in terms of scalability due to a partition-dependent condition. We prove that this condition is implied by its partition-independent version under a mild structural condition. This implication yields the second design strategy that is much more scalable than the first one. Finally, an experiment is conducted to demonstrate the MORP's flexibility, and two numerical examples are provided to illustrate its generality and compare both design strategies regarding scalability.