Finite-Time Consensus With Unknown Constant Delays via a Graph-Embedded Emulator

Abstract

This letter establishes exact finite-time average consensus for driftless agents with unknown, possibly heterogeneous constant actuation delays and a known common upper bound. A command emulator, initialized once from the physical state and driven by the undelayed command, reproduces the physical trajectories without delay knowledge. Since the plant is not measured thereafter, the scheme is an open-loop command generator with nominal exactness. Under zero-command initialization, a graph-embedded Lyapunov–Krasovskii functional, equivalently represented by the emulator, yields an exact Dini dissipation identity and delay-independent finite-time certificate. We establish the admissible edge-potential family, tightness condition, uncleared-buffer bias, extension to fully actuated driftless systems, exact quadratic command effort, and terminal-disagreement bounds under disturbances, delay mismatch, and initialization error. A mobile-cart study validates the delay-independent transient and predicted degradation.