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Distributed Matrix Pencil Formulations for Prescribed-Time Leader-Following Consensus of MASs with Unknown Sensor Sensitivity

Hefu Ye, Changyun Wen, Yongduan Song

TL;DR

This work tackles prescribed-time leader-following consensus for heterogeneous multi-agent systems with unknown sensor sensitivities. It combines a time-axis transformation with distributed state-feedback and output-feedback controllers and introduces a robust, distributed matrix-pencil design to contend with multiplicative noise, enabling convergence within a prescribed time $T$ while maintaining bounded gain in the practical setting. The paper provides two modes: exact prescribed-time tracking using an observer plus distributed controller, and a practical variant with bounded gains that yields convergence to a compact set before switching to a constant gain. Simulations on five single-link manipulators validate that all followers track the leader within the prescribed time, with observer errors vanishing and sensor heterogeneity accommodated by the proposed framework.

Abstract

In this paper, we address the problem of prescribed-time leader-following consensus of heterogeneous multi-agent systems (MASs) in the presence of unknown sensor sensitivity. Under a connected undirected topology, we propose a time-varying dual observer/controller design framework that makes use of regular local and inaccurate feedback to achieve consensus tracking within a prescribed time. In particular, the developed analysis framework is applicable to MASs equipped with sensors of different sensitivities. One of the design innovations involves constructing a distributed matrix pencil formulation based on worst-case sensors, yielding control parameters with sufficient robustness yet relatively low conservatism. Another novelty is the construction of the control gains, which consists of the product of a proportional coefficient obtained from the matrix pencil formulation and a classic time-varying function that grows to infinity or a novel bounded time-varying function. Furthermore, it is possible to extend the prescribed-time distributed protocol to infinite time domain by introducing the bounded time-varying gain technique without sacrificing the ultimate control accuracy, and the corresponding technical proof is comprehensive. The effectiveness of the method is demonstrated through a group of 5 single-link robot manipulators.

Distributed Matrix Pencil Formulations for Prescribed-Time Leader-Following Consensus of MASs with Unknown Sensor Sensitivity

TL;DR

This work tackles prescribed-time leader-following consensus for heterogeneous multi-agent systems with unknown sensor sensitivities. It combines a time-axis transformation with distributed state-feedback and output-feedback controllers and introduces a robust, distributed matrix-pencil design to contend with multiplicative noise, enabling convergence within a prescribed time while maintaining bounded gain in the practical setting. The paper provides two modes: exact prescribed-time tracking using an observer plus distributed controller, and a practical variant with bounded gains that yields convergence to a compact set before switching to a constant gain. Simulations on five single-link manipulators validate that all followers track the leader within the prescribed time, with observer errors vanishing and sensor heterogeneity accommodated by the proposed framework.

Abstract

In this paper, we address the problem of prescribed-time leader-following consensus of heterogeneous multi-agent systems (MASs) in the presence of unknown sensor sensitivity. Under a connected undirected topology, we propose a time-varying dual observer/controller design framework that makes use of regular local and inaccurate feedback to achieve consensus tracking within a prescribed time. In particular, the developed analysis framework is applicable to MASs equipped with sensors of different sensitivities. One of the design innovations involves constructing a distributed matrix pencil formulation based on worst-case sensors, yielding control parameters with sufficient robustness yet relatively low conservatism. Another novelty is the construction of the control gains, which consists of the product of a proportional coefficient obtained from the matrix pencil formulation and a classic time-varying function that grows to infinity or a novel bounded time-varying function. Furthermore, it is possible to extend the prescribed-time distributed protocol to infinite time domain by introducing the bounded time-varying gain technique without sacrificing the ultimate control accuracy, and the corresponding technical proof is comprehensive. The effectiveness of the method is demonstrated through a group of 5 single-link robot manipulators.
Paper Structure (11 sections, 7 theorems, 96 equations, 1 figure)

This paper contains 11 sections, 7 theorems, 96 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Problem formulation and preliminaries
  3. Preliminary result: State-feedback without unknown measurement sensitivity
  4. Main results: Output-feedback with unknown measurement sensitivity
  5. Prescribed-time exact consensus tracking
  6. Practical prescribed-time consensus tracking
  7. Simulations
  8. Conclusions
  9. Proof of Proposition 1
  10. Properties of two classes of matrix pencils
  11. A Lyapunov-like function

Key Result

Proposition 1

If the coordinate transformation (eta_k) is applied, and the transformed dynamic system (model-state) is asymptotically stabilized,For notational convenience, we drop the arguments of functions whenever no confusion will occur. where $r=be^{\tau}/T$ with $b \geq T$, $\mathbf{D}_c=\operatorname{diag}\{n,n-1,\cdots,1\}$, $\Phi_k=[\phi_{k,1},\cdots,\phi_{k,n}]^{\top}$ with $\phi_{k,i}=r^{n-i}(f_{k,i}

Figures (1)

  • Figure 1: States, control, and observer errors for MASs with the settling time $t_f+\delta=2$s under output feedback.

Theorems & Definitions (14)

  • Remark 1
  • Definition 1
  • Proposition 1
  • Theorem 1
  • Remark 2
  • Remark 3
  • Proposition 2
  • Theorem 2
  • Remark 4
  • Theorem 3
  • ...and 4 more