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

TL;DR

This paper introduces an energy-safe, iterative coupling method for parallel simulation of port-Hamiltonian systems that guarantees energy consistency and passivity, enabling adaptive accuracy and real-time performance.

Contribution

It proposes a novel Douglas--Rachford splitting scheme in scattering coordinates for energy-safe coupling, with proven passivity and convergence properties.

Findings

Passivity certificates hold at numerical roundoff levels.

State error decreases monotonically with more inner iterations.

Method supports energy-consistent real-time parallel simulation.

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.