Early-Terminable Energy-Safe Iterative Coupling for Parallel Simulation of Port-Hamiltonian Systems

2026-03-17

AI Summary

This work addresses the loss of power consistency in parallel simulation due to finite-iteration coupling, which can induce spurious energy exchange among passive subsystems. The authors propose an energy-safe, early-terminable iterative coupling method that, for the first time, models lossless interconnects as orthogonal constraints in the scattering (wave) domain and embeds them within a Douglas–Rachford splitting framework. By integrating discrete passivity conditions with impedance tuning, the approach rigorously guarantees discrete passivity at any finite number of iterations and provides an explicit residual bound. Benchmark tests on coupled oscillators demonstrate that passivity errors are reduced to double-precision round-off levels (≈1e⁻¹⁴), while the RMS state error monotonically decreases with inner iterations, confirming both energy consistency and convergence of the proposed method.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Security and Privacy: Large-scale security measurements

Abstract

Parallel simulation and control of large-scale robotic systems often rely on partitioned time stepping, yet finite-iteration coupling can inject spurious energy by violating power consistency--even when each subsystem is passive. This letter proposes a novel energy-safe, early-terminable iterative coupling for port-Hamiltonian subsystems by embedding a Douglas--Rachford (DR) splitting scheme in scattering (wave) coordinates. The lossless interconnection is enforced as an orthogonal constraint in the wave domain, while each subsystem contributes a discrete-time scattering port map induced by its one-step integrator. Under a discrete passivity condition on the subsystem time steps and a mild impedance-tuning condition, we prove an augmented-storage inequality certifying discrete passivity of the coupled macro-step for any finite inner-iteration budget, with the remaining mismatch captured by an explicit residual. As the inner budget increases, the partitioned update converges to the monolithic discrete-time update induced by the same integrators, yielding a principled, adaptive accuracy--compute trade-off, supporting energy-consistent real-time parallel simulation under varying computational budgets. Experiments on a coupled-oscillator benchmark validate the passivity certificates at numerical roundoff (on the order of 10e-14 in double precision) and show that the reported RMS state error decays monotonically with increasing inner-iteration budgets, consistent with the hard-coupling limit.

Problem

• port-Hamiltonian systems
• energy safety
• iterative coupling
• passivity
• parallel simulation

Innovation

• energy-safe coupling
• port-Hamiltonian systems
• Douglas–Rachford splitting
• discrete passivity
• scattering coordinates