Distributed Coordination Algorithms with Efficient Communication for Open Multi-Agent Systems with Dynamic Communication Links and Processing Delays

TL;DR

Three communication-efficient distributed algorithms designed for different scenarios solving the quantized averaging problem over the currently active node set under finite network openness and extending the approach for the case where nodes suffer from arbitrary bounded processing delays are proposed.

Abstract

In this paper we focus on the distributed quantized average consensus problem in open multi-agent systems consisting of dynamic directed communication links among active nodes. We propose three communication-efficient distributed algorithms designed for different scenarios. Our first algorithm solves the quantized averaging problem over the currently active node set under finite network openness (i.e., when the active set eventually stabilizes). Our second algorithm extends the aforementioned approach for the case where nodes suffer from arbitrary bounded processing delays. Our third algorithm operates over indefinitely open multi-agent networks with dynamic communication links (i.e., with continuous node arrivals and departures), computing the average that incorporates both active and historically active nodes. We analyze our algorithms' operation, establish their correctness, and present novel necessary and sufficient topological conditions ensuring their finite-time convergence. Numerical simulations on distributed sensor fusion for environmental monitoring demonstrate fast finite-time convergence and robustness across varying network sizes, departure/arrival rates, and processing delays. Finally, it is shown that our proposed algorithms compare favorably to algorithms in the existing literature.

Figures (4)

• Figure 1: Evolution of error $\varepsilon[k]$ (shown in \ref{['error_plot']}) over time $k$ averaged over $100$ random digraphs of $150$ potentially participating nodes, during the execution of QAOD, QAPOD, and QAIOD.
• Figure 2: Evolution of error $\varepsilon[k]$ (shown in \ref{['error_plot']}) over time $k$ averaged over $100$ random digraphs of $150, 300$, and $600$ potentially participating nodes, respectively, during the execution of QAOD, QAPOD, and QAIOD.
• Figure 3: Evolution of error $\varepsilon[k]$ (shown in \ref{['error_plot']}) over time $k$ averaged over $100$ random digraphs of $150$ potentially participating nodes for departing rates of $10\%$ and $50\%$, during the execution of QAOD, QAPOD, and QAIOD.
• Figure 4: Evolution of normalized errors $\varepsilon[k]$, and $\varepsilon^\prime[k]$ over time $k$, for a random digraph of $150$ potentially participating nodes, during the execution of QAOD, QAPOD, QAIOD, 2024:CDC_Themis_Open2024:CDC_Hadjic_Garcia.

Theorems & Definitions (5)

• Theorem 1
• Remark 1: Intuition of Theorem \ref{['main_convergence_condition_theorem']}
• Theorem 2
• Remark 2: Intuition of Theorem \ref{['main_convergence_condition_theorem_process_delays']}
• Theorem 3