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 $ \mathcal{O}(N) $ per-agent complexity under a bounded-ADMM-iteration proviso.
Citation: Vladimir Stojanovic, Ljubisa Dubonjic, Sasa Prodanovic. Distributed barrier iterative learning control for networked Euler–Lagrange systems under time-varying delays[J]. Mathematical Modelling and Control, 2026, 6(3): 290-300. doi: 10.3934/mmc.2026022
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 $ \mathcal{O}(N) $ per-agent complexity under a bounded-ADMM-iteration proviso.
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Vladimir Stojanovic, Ljubisa Dubonjic, Sasa Prodanovic. Distributed barrier iterative learning control for networked Euler–Lagrange systems under time-varying delays[J]. Mathematical Modelling and Control, 2026, 6(3): 290-300. doi: 10.3934/mmc.2026022
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