ChronoSync: A Decentralized Chronometer Synchronization Protocol for Multi-Agent Systems

TL;DR

ChronoSync addresses decentralized time synchronization in multi-agent systems by equipping each agent with a hardware clock $\theta_p$ and a steerable software clock $\vartheta_p$, and by formulating a hybrid closed-loop model that accommodates intermittent, directed communication. The authors develop a distributed controller that simultaneously estimates each clock's unknown drift $a_p$ and drives software clocks toward a common drift $a^{\star}$ while ensuring $\vert\vartheta_p-\vartheta_q\vert \le \nu$ within a global GPES framework. A Lyapunov-based stability analysis of the resulting hybrid system yields conditions under which the synchronization set is globally practically exponentially stable and provides a practical LMI-based method to certify these conditions. Simulation with 12 agents demonstrates convergence of drift to $a^{\star}$ and synchronization within $\nu$, validating the theoretical guarantees and showing robustness to bounded disturbances and asynchronous broadcasts. ChronoSync thus offers a scalable, robust, and communication-efficient approach to time synchronization in MASs, with potential extensions to delays, dropouts, and switching communication topologies.

Abstract

This work presents a decentralized time synchronization algorithm for multi-agent systems. Each agent possesses two clocks, a hardware clock that is perturbed by environmental phenomena (e.g., temperature, humidity, pressure, g forces, etc.) and a steerable software clock that inherits the perturbations affecting the hardware clock. Under these disturbances and the independent time kept by the hardware clocks, our consensus-based controller enables all agents to steer their software-defined clocks into practical synchronization while achieving a common user-defined clock drift. Furthermore, we treat the drift of each hardware clock as an unknown parameter, which our algorithm can accurately estimate. The coupling of the agents is modeled by a connected, undirected, and static graph. However, each agent possesses a timer mechanism that determines when to broadcast a sample of its software time and update its own software-time estimate. Hence, communication between agents can be directed, intermittent, and asynchronous. The closed-loop dynamics of the ensemble is modeled using a hybrid system, where a Lyapunov-based stability analysis demonstrates that a set encoding the time synchronization and clock drift estimation objectives is globally practically exponentially stable. The performance suggested by the theoretical development is confirmed in simulation.

Figures (6)

• Figure 1: Depiction of the trajectories of the software-defined times, $\{\phi_{\vartheta_p}(t,j)\}_{p\in\mathcal{V}}$. The left inset plot shows the software-defined time trajectories during the beginning of the simulation, while the right inset plot shows the software-defined time trajectories during the end of the simulation.
• Figure 2: Illustration of the trajectories of the software-defined time drifts, i.e., $\{\phi_{\dot{\vartheta}_p}(t,j)\}_{p\in\mathcal{V}}$. The main plot shows the drift trajectories during the beginning of the simulation; the inset plot shows the drift trajectories during the second half of the simulation. The black dashed line is the graph of the function $t\mapsto a^{\star}=1$, representing the desired drift, in both plots. For each agent of the MAS, the drift trajectory converges to $[1-\epsilon,1+\epsilon]$ with $\epsilon = 2.27\times 10^{-5}$.
• Figure 3: Illustration of the trajectories of the hardware clock drift estimation error, i.e., $\{\phi_{\tilde{a}_p}(t,j)\}_{p\in\mathcal{V}}$ The main plots depicts the drift estimation error trajectories during the beginning of the simulation; the inset plots shows the drift estimation error trajectories during the second half of the simulation. For each agent of the MAS, the drift estimation error trajectory converges to $[-\epsilon,\epsilon]$ with $\epsilon = 3.06\times 10^{-6}$.
• Figure 4: Depiction of the trajectories of the hardware clock estimation errors, $\{\phi_{\tilde{\theta}_p}(t,j)\}_{p\in\mathcal{V}}$. The main plot shows the hardware clock estimation error trajectories during the beginning of the simulation; the inset plot shows the hardware clock estimation error trajectories during the second half of the simulation. For each agent of the MAS, the hardware clock estimation error trajectory converges to the set $[-\epsilon,\epsilon]$ with $\epsilon = 1.18\times 10^{-6}$.
• Figure 5: The blue line depicts the trajectory of the distance between the solution $\phi$ of the closed-loop hybrid system $\mathcal{H}$ and the set $\mathcal{A}$. The magenta line represents the trajectory of the disagreement metric $\Vert\eta\Vert$ along the solution $\phi$. The red dashed line is the graph of the function $t\mapsto \nu=0.06$, representing the desired time synchronization tolerance. The horizontal axis uses a linear scale, and the vertical axis uses a logarithmic scale. Both trajectories are bounded above by $8\times 10^{-6}$ for $t\geq 80$ seconds.

Theorems & Definitions (11)

• Lemma 1
• Lemma 2
• proof
• Definition 1
• Definition 2
• Lemma 3
• proof
• Theorem 1
• proof
• Corollary 1