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Full-State Prescribed Performance-Based Consensus of Double-Integrator Multi-Agent Systems with Jointly Connected Topologies

Yahui Hou, Bin Cheng

TL;DR

This work tackles consensus for MAS with double-integrator dynamics under jointly connected switching topologies while enforcing full-state prescribed performance on both relative positions $y_l(t)$ and relative velocities $z_l(t)$. It introduces a distributed PPC controller that combines two nonlinear error transformations, $\\varepsilon_{y}$ and $\\varepsilon_{z}$, and a topology-robust law $u_i(t)$ to keep errors within time-varying bounds $-\\rho_{y,l}(t)<y_l(t)<\\rho_{y,l}(t)$ and $-\\rho_{z,l}(t)<z_l(t)<\\rho_{z,l}(t)$, ensuring asymptotic consensus. The main contributions include guaranteeing independent PPC bounds on full state, enabling topology-agnostic parameter design, handling general graphs with cycles, and providing a rigorous four-phase stability proof that leverages Barbalat’s lemma. A numerical simulation corroborates the theoretical results, showing confinement within prescribed regions and eventual consensus despite topology switching. This work advances precise transient performance control in distributed multi-robot systems operating over dynamically changing communication networks.

Abstract

This paper addresses the full-state prescribed performance-based consensus problem for double-integrator multi-agent systems with jointly connected topologies. To improve the transient performance, a distributed prescribed performance control protocol consisting of the transformed relative position and the transformed relative velocity is proposed, where the communication topology satisfies the jointly connected assumption. Different from the existing literatures, two independent transient performance specifications imposed on relative positions and relative velocities can be guaranteed simultaneously. A numerical example is ultimately used to validate the effectiveness of proposed protocol.

Full-State Prescribed Performance-Based Consensus of Double-Integrator Multi-Agent Systems with Jointly Connected Topologies

TL;DR

This work tackles consensus for MAS with double-integrator dynamics under jointly connected switching topologies while enforcing full-state prescribed performance on both relative positions and relative velocities . It introduces a distributed PPC controller that combines two nonlinear error transformations, and , and a topology-robust law to keep errors within time-varying bounds and , ensuring asymptotic consensus. The main contributions include guaranteeing independent PPC bounds on full state, enabling topology-agnostic parameter design, handling general graphs with cycles, and providing a rigorous four-phase stability proof that leverages Barbalat’s lemma. A numerical simulation corroborates the theoretical results, showing confinement within prescribed regions and eventual consensus despite topology switching. This work advances precise transient performance control in distributed multi-robot systems operating over dynamically changing communication networks.

Abstract

This paper addresses the full-state prescribed performance-based consensus problem for double-integrator multi-agent systems with jointly connected topologies. To improve the transient performance, a distributed prescribed performance control protocol consisting of the transformed relative position and the transformed relative velocity is proposed, where the communication topology satisfies the jointly connected assumption. Different from the existing literatures, two independent transient performance specifications imposed on relative positions and relative velocities can be guaranteed simultaneously. A numerical example is ultimately used to validate the effectiveness of proposed protocol.
Paper Structure (8 sections, 4 theorems, 33 equations, 3 figures)

This paper contains 8 sections, 4 theorems, 33 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Background and Problem Formulation
  3. Notations and Graph Theory
  4. Prescribed Performance Control
  5. Problem Formulation
  6. Main Results
  7. Simulation
  8. Conclusion

Key Result

Lemma 1

Given any positive constants $k$ and $D$, we have for all $\|\varepsilon_s(\hat{s})\| > \bar{\varepsilon}_s$, with constant $\bar{\varepsilon}_s > 0$.

Figures (3)

  • Figure 1: Topology graphs. (a) $\bar{\mathcal{G}}_1$. (b) $\bar{\mathcal{G}}_2$. (c) $\bar{\mathcal{G}}_3$.
  • Figure 2: Convergence trajectories with prescribed performance. Top: relative positions; bottom: relative velocities.
  • Figure 3: State trajectories of all agents. Top: position trajectories; bottom: velocity trajectories.

Theorems & Definitions (7)

  • Lemma 1: stamouli2022robust
  • Remark 1
  • Lemma 2: Hou2023EventHou2023Prescribed
  • Lemma 3: Hou2023EventHou2023Prescribed
  • Theorem 1
  • Remark 2
  • Remark 3