Multi-Partite Output Regulation of Multi-Agent Systems

TL;DR

This work introduces MORP, a general framework for multi-agent systems that extends beyond cooperative and bipartite objectives by employing a graph-independent $k$-partition transformation to define arbitrary partitions of the node set. It shows how MORP can be realized as a CORP via a feedforward-based distributed controller and presents two design strategies: a partition-dependent design that recomputes regulator solutions for each partition term, and a partition-independent design that uses an auxiliary LME to achieve greater scalability with matched disturbances. The paper provides necessary and sufficient solvability conditions, along with partition-independent sufficiency results and explicit constructions for controller gains, enabling scalable deployment across dynamic mission objectives. Experimental and numerical illustrations demonstrate MORP’s flexibility in sequential objectives and its scalability advantages, particularly for large numbers of partitions, while highlighting tradeoffs in disturbance assumptions. Overall, MORP offers a flexible, scalable approach to encoding and achieving multiple, shifting objectives in heterogeneous MASs, with practical implications for defense, search-and-rescue, and autonomous coordination.

Abstract

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.

Figures (3)

• Figure 1: The trajectories of the MAS. Here, $y_{ij}$ denotes the $j$th entry of follower $i$'s output for $i=1,2,3$ and $y_{0j}$ denotes the $j$th entry of $v$ while "$\times$" and "o" marks $y_{ij}$ at the initial and final times for $i=0,1,2,3$, respectively.
• Figure 2: The top row depicts the identical output responses with the design in 9089253 and the proposed design. The bottom row presents the output responses with the proposed formulation for 2 BORPs that are impossible to formulate with the approach in 9089253 without altering the underlying graph.
• Figure 3: Elapsed times of both design strategies with respect to the cardinality $M$ of the given set of $k$-partition transformation terms.

Theorems & Definitions (25)

• Definition 1: Sections 1.10, 5.1, and 5.4 in combinatorix
• Definition 2
• Lemma 1
• Remark 1
• Remark 2
• Lemma 2
• Remark 3
• Remark 4
• Theorem 1
• Remark 5