Delay-Robust Primal-Dual Dynamics for Distributed Optimization
This addresses robustness issues in distributed optimization for systems prone to delays, but it is incremental as it builds on existing primal-dual dynamics.
The paper tackles the problem of communication delays in continuous-time primal-dual gradient dynamics for distributed optimization by proposing a delay-robust version with an auxiliary state and gain matrix, achieving uniform asymptotic stability under bounded, time-varying delays as demonstrated numerically.
Continuous-time primal-dual gradient dynamics (PDGD) is an ubiquitous approach for dynamically solving constrained distributed optimization problems. Yet, the distributed nature of the dynamics makes it prone to communication uncertainties, especially time delays. To mitigate this effect, we propose a delay-robust continuous-time PDGD. The dynamics is obtained by augmenting the standard PDGD with an auxiliary state coupled through a gain matrix, while preserving the optimal solution. Then, we present sufficient tuning conditions for this gain matrix in the form of linear matrix inequalities, which ensure uniform asymptotic stability in the presence of bounded, time-varying delays. The criterion is derived via the Lyapunov-Krasovskii method. A numerical example illustrates the improved delay robustness of our approach compared to the standard PDGD under large, time-varying delays.