Distributed barrier iterative learning control for networked Euler–Lagrange systems under time-varying delays

Abstract

Coordinated trajectory tracking in networks of robotic manipulators is fundamental to collaborative automation, yet strict joint-velocity limits and network-induced communication delays frequently cause standard controllers to violate safety constraints or diverge. Existing decentralized iterative learning control (ILC) methods fail here because they rely on scalar first-order dynamics and centralized topologies, which cannot handle coupled second-order Euler–Lagrange (E-L) dynamics and asynchronous time-varying delays. A distributed time-varying barrier Lyapunov function (TV-BLF) norm-optimal ILC framework is therefore developed. Embedding the TV-BLF into a distributed alternating direction method of multipliers (ADMM) cost and constructing a composite Lyapunov-Krasovskii functional compensates communication delays while strictly enforcing velocity constraints. Under the standard nonlifted ILC sensitivity approximation, a quantitative margin argument establishes semi-globally uniformly ultimately bounded (SGUUB) stability with explicit delay-dependent bounds, closing the invariance gap of a purely qualitative barrier argument. Monte Carlo simulations on a heterogeneous fleet of 2-DoF manipulators show a statistically significant reduction in mean squared error (MSE) and zero constraint violations versus three baselines, while preserving O(N) per-agent complexity under a bounded-ADMM-iteration proviso.