Delay-Robust Primal-Dual Dynamics for Distributed Optimization
Abstract
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.
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Cited by
Still being checked.
- Authors
- Şen, G. D., Machado, J. E., Öke Günel, G., & Schiffer, J.
- Affiliations
- Brandenburg University of Technology Cottbus-Senftenberg (DE)
- Istanbul Technical University, Istanbul, Türkiye
- Venue
- IEEE Control Systems Letters
- Published
- 2026
- Volume
- 10
- Pages
- 469-474
- ISSN
- 2475-1456 (ISSN-L)
- OpenAlex
- W7163029760
- Semantic Scholar
- 731b70e70423669d29fe99bb5cb71dd62261652b
- Cited by
- 0
- References
- 25
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- IEEE Control Systems Letters (publishedVersion)
- Istanbul Technical University Academic Open Archive (Istanbul Technical University) (submittedVersion)
- Fraunhofer-Publica (Fraunhofer-Gesellschaft) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Networks and Communications › Distributed Control Multi-Agent Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Optimization
- Keywords
- distributed optimization, time delay, delay robustness, continuous-time dynamics, auxiliary state, linear matrix inequalities, uniform asymptotic stability, time-varying delays, Lyapunov-Krasovskii functional, communication uncertainty
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