Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

One-bit consensus of controllable linear multi-agent systems with communication noises

Ru An, Ying Wang, Yanlong Zhao, Ji-Feng Zhang

TL;DR

This work addresses one-bit consensus in controllable linear multi-agent systems with communication noise. It introduces a linear compression encoding to realize a one-bit data rate and a stabilization-plus-decay consensus controller with a recursive estimator to recover neighbor states from one-bit data. Two coupled Lyapunov functions are developed to analyze the joint evolution of compressed-state consensus and estimation error, establishing mean-square consensus at a rate $O(\tfrac{1}{t})$ for connected fixed topologies and extending the results to jointly connected Markovian switching topologies via an equivalence to a fixed topology. Numerical simulations on a seven-aircraft altitude coordination problem validate the theory and demonstrate robustness to topology switching.

Abstract

This paper addresses the one-bit consensus of controllable linear multi-agent systems (MASs) with communication noises. A consensus algorithm consisting of a communication protocol and a consensus controller is designed. The communication protocol introduces a linear compression encoding function to achieve a one-bit data rate, thereby saving communication costs. The consensus controller with a stabilization term and a consensus term is proposed to ensure the consensus of a potentially unstable but controllable MAS. Specifically, in the consensus term, we adopt an estimation method to overcome the information loss caused by one-bit communications and a decay step to attenuate the effect of communication noise. Two combined Lyapunov functions are constructed to overcome the difficulty arising from the coupling of the control and estimation. By establishing similar iterative structures of these two functions, this paper shows that the MAS can achieve consensus in the mean square sense at the rate of the reciprocal of the iteration number under the case with a connected fixed topology. Moreover, the theoretical results are generalized to the case with jointly connected Markovian switching topologies by establishing a certain equivalence relationship between the Markovian switching topologies and a fixed topology. Two simulation examples are given to validate the algorithm.

One-bit consensus of controllable linear multi-agent systems with communication noises

TL;DR

This work addresses one-bit consensus in controllable linear multi-agent systems with communication noise. It introduces a linear compression encoding to realize a one-bit data rate and a stabilization-plus-decay consensus controller with a recursive estimator to recover neighbor states from one-bit data. Two coupled Lyapunov functions are developed to analyze the joint evolution of compressed-state consensus and estimation error, establishing mean-square consensus at a rate for connected fixed topologies and extending the results to jointly connected Markovian switching topologies via an equivalence to a fixed topology. Numerical simulations on a seven-aircraft altitude coordination problem validate the theory and demonstrate robustness to topology switching.

Abstract

This paper addresses the one-bit consensus of controllable linear multi-agent systems (MASs) with communication noises. A consensus algorithm consisting of a communication protocol and a consensus controller is designed. The communication protocol introduces a linear compression encoding function to achieve a one-bit data rate, thereby saving communication costs. The consensus controller with a stabilization term and a consensus term is proposed to ensure the consensus of a potentially unstable but controllable MAS. Specifically, in the consensus term, we adopt an estimation method to overcome the information loss caused by one-bit communications and a decay step to attenuate the effect of communication noise. Two combined Lyapunov functions are constructed to overcome the difficulty arising from the coupling of the control and estimation. By establishing similar iterative structures of these two functions, this paper shows that the MAS can achieve consensus in the mean square sense at the rate of the reciprocal of the iteration number under the case with a connected fixed topology. Moreover, the theoretical results are generalized to the case with jointly connected Markovian switching topologies by establishing a certain equivalence relationship between the Markovian switching topologies and a fixed topology. Two simulation examples are given to validate the algorithm.

Paper Structure

This paper contains 24 sections, 15 theorems, 88 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Background and motivation
  3. Related literature
  4. Main contribution
  5. Preliminaries and problem formulation
  6. Basic concept
  7. Graph theory
  8. Problem formulation
  9. Algorithm design
  10. Main resluts
  11. Properties of compressed states and their estimates
  12. Consensus of the original states
  13. Consensus of the MAS under Markovian switching communication networks
  14. Numerical Simulation
  15. Conclusion
  16. ...and 9 more sections

Key Result

Lemma 1

( hu-consensus-SCIS2022). If Assumption assm-G holds, then matrix $L$ has these properties:

Figures (7)

  • Figure 1: The fixed communication topology of the multi-agent system
  • Figure 2: A schematic diagram of an aircraft
  • Figure 3: The altitude trajectory of each aircraft under fixed topology
  • Figure 4: The trajectory of the log(MSEs) under fixed topology
  • Figure 5: The Markovian switching communication topologies
  • ...and 2 more figures

Theorems & Definitions (41)

  • Remark 1
  • Remark 2
  • Definition 1
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Remark 7
  • Lemma 1
  • Lemma 2
  • ...and 31 more