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Propensity Formation-Containment Control of Fully Heterogeneous Multi-Agent Systems via Online Data-Driven Learning

Ao Cao, Fuyong Wang, Zhongxin Liu

TL;DR

This work tackles Propensity Formation-Containment Control (PFCC) in fully heterogeneous multi-agent systems by introducing propensity factors and the Influential Transit Formation Leader (ITFL) to exploit leader information across complex topologies. It combines distributed adaptive observers with a model-based PFCC controller and a novel online data-driven learning algorithm that obviates the need for explicit system models. The approach guarantees asymptotic convergence of follower states to formations defined by propensity-weighted leader signals, even under ITFL constraints and without precise models, demonstrated through numerical simulations. This yields a scalable, data-driven framework for formation-containment in heterogeneous MAS with practical significance for coordinated multi-robot or multi-vehicle systems.

Abstract

This paper introduces an online data-driven learning scheme designed to address a novel problem in propensity formation and containment control for fully heterogeneous multi-agent systems. Unlike traditional approaches that rely on the eigenvalues of the Laplacian matrix, this problem considers the determination of follower positions based on propensity factors released by leaders. To address the challenge of incomplete utilization of leader information in existing multi-leader control methods, the concept of an influential transit formation leader (ITFL) is introduced. An adaptive observer is developed for the agents, including the ITFL, to estimate the state of the tracking leader or the leader's formation. Building on these observations, a model-based control protocol is proposed, elucidating the relationship between the regulation equations and control gains, ensuring the asymptotic convergence of the agent's state. To eliminate the necessity for model information throughout the control process, a new online data-driven learning algorithm is devised for the control protocol. Finally, numerical simulation results are given to verify the effectiveness of the proposed method.

Propensity Formation-Containment Control of Fully Heterogeneous Multi-Agent Systems via Online Data-Driven Learning

TL;DR

This work tackles Propensity Formation-Containment Control (PFCC) in fully heterogeneous multi-agent systems by introducing propensity factors and the Influential Transit Formation Leader (ITFL) to exploit leader information across complex topologies. It combines distributed adaptive observers with a model-based PFCC controller and a novel online data-driven learning algorithm that obviates the need for explicit system models. The approach guarantees asymptotic convergence of follower states to formations defined by propensity-weighted leader signals, even under ITFL constraints and without precise models, demonstrated through numerical simulations. This yields a scalable, data-driven framework for formation-containment in heterogeneous MAS with practical significance for coordinated multi-robot or multi-vehicle systems.

Abstract

This paper introduces an online data-driven learning scheme designed to address a novel problem in propensity formation and containment control for fully heterogeneous multi-agent systems. Unlike traditional approaches that rely on the eigenvalues of the Laplacian matrix, this problem considers the determination of follower positions based on propensity factors released by leaders. To address the challenge of incomplete utilization of leader information in existing multi-leader control methods, the concept of an influential transit formation leader (ITFL) is introduced. An adaptive observer is developed for the agents, including the ITFL, to estimate the state of the tracking leader or the leader's formation. Building on these observations, a model-based control protocol is proposed, elucidating the relationship between the regulation equations and control gains, ensuring the asymptotic convergence of the agent's state. To eliminate the necessity for model information throughout the control process, a new online data-driven learning algorithm is devised for the control protocol. Finally, numerical simulation results are given to verify the effectiveness of the proposed method.

Paper Structure

This paper contains 11 sections, 10 theorems, 46 equations, 8 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation
  4. Background Knowledge
  5. Problem Formulation
  6. Main Results
  7. Model-Based Control Method for PFCC Problem
  8. Data-Based Distributed Adaptive Observer
  9. Online Data-Driven Learning Method for PFCC Problem
  10. Simulation results
  11. Conclusions

Key Result

Lemma 1

(Woodbury Matrix Identity higham2002accuracy). If $Z \in {\mathbb{R}^{n \times n}}$ and $W\in{\mathbb{R}^{n \times n}}$ are invertible matrices, $U\in{\mathbb{R}^{n \times l}}$ and $V\in{\mathbb{R}^{l \times n}}$ are conformable matrices, then $(Z + U W V)^{-1} = Z^{-1} - Z^{-1} U (W^{-1} + V Z^{-1}

Figures (8)

  • Figure 1: Example of the influence of propensity factors on follower convergence positions under different timestamps.
  • Figure 2: Examples to describe IFLs and ITFLs.
  • Figure 3: Network topology composed of all agents.
  • Figure 4: Sum of the norm of all observer errors for agents. (a). Observer error $||\tilde{x}_m^o||+\sum\nolimits_{q \in {\mathcal{N}}_{m}^L} {||\tilde{h}_m^q||}$ for leaders. (b). Observer error $||\tilde{x}_m^o||+\sum\nolimits_{q \in {\mathcal{N}}_{m}^F} {||\tilde{h}_m^q||}$ for followers.
  • Figure 5: Norm of errors for PFCC problem. (a). Formation error of leaders $||e_q^l||$in \ref{['58']}. (b). Propensity containment error of followers $||e_i^f||$ in \ref{['60']}.
  • ...and 3 more figures

Theorems & Definitions (24)

  • Lemma 1
  • Lemma 2
  • Remark 1
  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Remark 2
  • Definition 5
  • Definition 6
  • ...and 14 more