Continuous-Time Optimization Dynamics Mirroring ADMM Architecture and Passivity-Based Robustification against Delays

This article addresses a convex optimization problem that suffers from communication delays between a central collector and subsystems. First, we introduce continuous-time optimization dynamics that mirror the alternating direction method of multipliers architecture. Furthermore, we reveal that the proposed optimization dynamics have an architecture similar to that of bilateral teleoperation systems. By virtue of this passivity-based perspective, we apply a scattering transformation, which compensates for communication delays. Finally, we demonstrate the effectiveness of the proposed dynamics through numerical simulations of a grasp force optimization problem.