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On two-degrees-of-freedom agreement protocols

Gal Barkai, Leonid Mirkin, Daniel Zelazo

TL;DR

The paper addresses robust agreement in multi-agent systems under measurement noise and disturbances. It introduces a distributed two-degrees-of-freedom (2DOF) agreement protocol that decouples network filtering from local feedback, enabling independent design of the network filter and accommodating heterogeneous agents. The approach yields improved noise attenuation and disturbance rejection compared to standard diffusive consensus, with theoretical agreement conditions and practical network-filter design rules demonstrated through numerical examples. Overall, the 2DOF framework offers a promising, modular alternative to conventional consensus, with potential extensions to uncertainties and transmission delays.

Abstract

We propose a distributed two-degrees-of-freedom (2DOF) architecture for driving autonomous, possibly heterogeneous, agents to agreement. The scheme mirrors classical servo structures, separating local feedback from network filtering. This separation enables independent network-filter design for prescribed noise attenuation and allows controller heterogeneity to reject local disturbances, including disturbances exciting unstable agreement poles -- which is known to be impossible via standard diffusive couplings. The potential of the framework is illustrated via two numerical examples.

On two-degrees-of-freedom agreement protocols

TL;DR

The paper addresses robust agreement in multi-agent systems under measurement noise and disturbances. It introduces a distributed two-degrees-of-freedom (2DOF) agreement protocol that decouples network filtering from local feedback, enabling independent design of the network filter and accommodating heterogeneous agents. The approach yields improved noise attenuation and disturbance rejection compared to standard diffusive consensus, with theoretical agreement conditions and practical network-filter design rules demonstrated through numerical examples. Overall, the 2DOF framework offers a promising, modular alternative to conventional consensus, with potential extensions to uncertainties and transmission delays.

Abstract

We propose a distributed two-degrees-of-freedom (2DOF) architecture for driving autonomous, possibly heterogeneous, agents to agreement. The scheme mirrors classical servo structures, separating local feedback from network filtering. This separation enables independent network-filter design for prescribed noise attenuation and allows controller heterogeneity to reject local disturbances, including disturbances exciting unstable agreement poles -- which is known to be impossible via standard diffusive couplings. The potential of the framework is illustrated via two numerical examples.

Paper Structure

This paper contains 10 sections, 3 theorems, 47 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Classical control architectures
  4. Consensus protocol revisited
  5. A two-degrees-of-freedom agreement protocol
  6. Numerical examples
  7. Design of a network filter
  8. Design and performance for noise
  9. Design for disturbance rejection
  10. Concluding remarks

Key Result

Proposition III.1

Let $P\coloneqq \mathop{\mathrm{diag}}\nolimits\{P_i\}$ and $R\coloneqq \mathop{\mathrm{diag}}\nolimits\{R_i\}$ denote the aggregate plants and local controllers respectively. The 2DOF consensus protocol is given by

Figures (6)

  • Figure 1: Classical servo-regulation control architectures.
  • Figure 2: A Two-Degrees-of-Freedom agreement protocol.
  • Figure 3: The underlying communication graph for the examples in §\ref{['sec:2dof:ex']}.
  • Figure 4: Simulations of the control designs for the example in § \ref{['sec:ex:noise']}(solid: 2DOF design, dashed: standard consensus protocol).
  • Figure 5: The output trajectories of controllers from the example in § \ref{['sec:ex:noise']} for a step disturbance applied to agent $1$ at $t=5$.
  • ...and 1 more figures

Theorems & Definitions (6)

  • Proposition III.1
  • proof
  • Theorem III.2
  • proof
  • Proposition III.3
  • proof