Skip to main content
SpringerLink
Log in

Distributed Optimization over General Directed Networks with Random Sleep Scheme

  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

Distributed optimization aims at optimizing a global objective function which is described by a sum of local objective functions through local information processing and sharing. This paper studies the problem of distributed optimization over a network in which underlying graph is generally directed strongly connected. Most existing distributed algorithms require each agent to observe the gradient of the local objective function per iteration, which leads to heavy computational cost. A computation-efficient distributed optimization algorithm incorporating random sleep scheme is proposed by incorporating rescaling gradient technique to address the unbalancedness of the directed graph. The implementation of the proposed algorithm allows agents not only locally allocates the weights on the received information, but also independently decides whether to execute gradient observation at each iteration. Theoretical analysis verifies that the proposed algorithm is able to seek the optimal solution with probability one. Simulations are shown to demonstrate effectiveness of the proposed algorithm, show correctness of the theoretical analysis, and investigate the tradeoffs between convergence performance and computation cost.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Dong, Q. Ai, and S. He, “Observer-based proportional-integral controller design for a class of uncertain switched systems” Iranian Journal of Science and Technology, Transactions of Electrical Engineering, vol. 43, no. 1, pp. 303–312, 2019.

    Article  Google Scholar 

  2. J. Huang, L. Chen, X. Xie, M. Wang, B. Xu, “Distributed event-triggered consensus control for heterogeneous multiagent systems under fixed and switching topologies,” International Journal of Control Automation and Systems, vol. 17, no. 8, pp. 1945–1956, 2019.

    Article  Google Scholar 

  3. S. He, J. Song, and F. Liu, “Robust finite-time bounded controller design of time-delay conic nonlinear systems using sliding mode control strategy,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 11, pp. 1863–1873, 2018.

    Article  Google Scholar 

  4. W. He, Z. Yan, C. Sun, and Y. Chen, “Adaptive neural network control of a flapping wing micro aerial vehicle with disturbance observer,” IEEE Transactions on Cybernetics, vol. 47, no. 10, pp. 3452–3465, 2017.

    Article  Google Scholar 

  5. H. Li, X. Liao, G. Chen, Z. Dong, D. J. Hill, and T. Huang, “Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks,” Neural Networks, vol. 66, pp. 1–10, 2015.

    Article  MATH  Google Scholar 

  6. H. Gao, W. He, C. Zhou, and C. Sun, “Neural network control of a two-link flexible robotic manipulator using assumed mode method,” IEEE Transactions on Industrial Informatics, vol. 15, no. 2, pp. 755–765, 2019.

    Article  Google Scholar 

  7. S. He, Q. Ai, C. Ren, J. Dong, and F. Liu, “Finite-time resilient controller design of a class of uncertain nonlinear systems with time-delays under asynchronous switching,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 49, no. 2, pp. 281–286, 2019.

    Article  Google Scholar 

  8. C. Sun, W. He, and J. Hong, “Neural network control of a flexible robotic manipulator using the lumped spring-mass model,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 8, pp. 1863–1874, 2017.

    Article  Google Scholar 

  9. H. Li, X. Liao, T. Huang, W. Zhu, and Y. Liu, “Second-order global consensus in multiagent networks with random directional link failure,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 3, pp. 565–575, March 2015.

    Article  MathSciNet  Google Scholar 

  10. T. Wang, H. Fu, J. Li, Y. Zhang, X. Zhou, X. Chen, “Optimal consensus control for heterogeneous nonlinear multiagent systems with partially unknown dynamics,” International Journal of Control Automation and Systems, vol. 17, no. 9, pp. 2400–2413, 2019.

    Article  Google Scholar 

  11. L. Xiao, M. Johansson, and S. P. Boyd, “Simultaneous routing and resource allocation via dual decomposition,” IEEE Transactions on Communications, vol. 52, no. 7, pp. 1136–1144, 2004.

    Article  Google Scholar 

  12. J. Zhang, D. Qi, and M. Yu, “A game theoretic approach for the distributed control of multi-agent systems under directed and time-varying topology,” International Journal of Control, Automation, and Systems, vol. 12, no. 4, pp. 749–758, 2014.

    Article  Google Scholar 

  13. S. Pereira and A. Pages-Zamora, “Consensus in correlated random wireless sensor networks,” IEEE Transactions on Signal Processing, vol. 59, no. 12, pp. 6279–6284, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  14. K. Oh and H. Ahn, “Distributed formation control based on orientation alignment and position estimation,” International Journal of Control, Automation, and Systems, vol. 16, no. 3, pp. 1112–1119, 2018.

    Article  Google Scholar 

  15. A. Nedić and A. Ozdaglar, “Distributed subgradient methods for Multiagent optimization,” IEEE Transactions on Automatic Control, vol. 54, no. 1, pp. 48–61, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. Duchi, A. Agarwal, and M. Wainwright, “Dual averaging for distributed optimization: Convergence analysis and network scaling,” IEEE Transactions on Automatic Control, vol. 57, no. 3, pp. 592–606, Mar. 2012.

    Article  MathSciNet  MATH  Google Scholar 

  17. A. Nedić and A. Olshevsky, “Distributed optimization over time-varying directed graphs,” IEEE Transactions on Automatic Control, vol. 60, no. 3, pp. 601–615, 2014.

    Article  MathSciNet  MATH  Google Scholar 

  18. I. Matei and J. S. Baras, “Performance evaluation of the consensus-based distributed subgradient method under random communication topologies,” IEEE Journal of Selected Topics in Signal Processing, vol. 5, no. 4, pp. 754–771, 2011.

    Article  Google Scholar 

  19. M. Zhu and S. Martinez, “On distributed convex optimization under inequality and equality constraints,” IEEE Transactions on Automatic Control, vol. 57, no. 1, pp. 151–164, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  20. W. Shi, Q. Ling, G. Wu, and W. Yin, “Extra: An exact firstorder algorithm for decentralized consensus optimization,” SIAM Journal on Optimization, vol. 25, no. 2, pp. 944–966, 2015.

    Article  MathSciNet  MATH  Google Scholar 

  21. G. Qu and N. Li, “Harnessing smoothness to accelerate distributed optimization,” IEEE Transactions on Control of Network Systems, vol. 5, no. 3, pp. 1245–1260, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  22. J. Xu, S. Zhu, Y. C. Soh, and L. Xie, “Augmented distributed gradient methods for multi-agent optimization under uncoordinated constant stepsizes,” Proceedings of IEEE 54th Annual Conference on Decision and Control, pp. 2055–2060, 2015.

  23. A. Nedić, A. Olshevsky, and S Wei, “Achieving geometric convergence for distributed optimization over time-varying graphs,” SIAM Journal on Optimization, vol. 27, no. 4, pp. 2597–2633, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  24. M. Zhu and S. Martínez, “Discrete-time dynamic average consensus,” Automatica, vol. 46, no. 2, pp. 322–329, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  25. J. Xu, S. Zhu, Y. C. Soh, and L. Xie, “Convergence of asynchronous distributed gradient methods over stochastic networks,” IEEE Transactions on Automatic Control, vol. 63, no. 2, pp. 434–448, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  26. A. Nedić, A. Olshevsky, W. Shi, and C. A. Uribe, “Geometrically convergent distributed optimization with uncoordinated stepsizes,” Proceedings of the American Control Conference, 2017. DOI: https://doi.org/10.23919/ACC.2017.7963560

  27. C. Xi and U. A. Khan, “Distributed subgradient projection algorithm over directed graphs,” IEEE Transactions on Automatic Control, vol. 62, no. 8, pp. 3986–3992, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  28. C. Xi, R. Xin, and U. A. Khan, “ADD-OPT: Accelerated distributed directed optimization,” IEEE Transactions on Automatic Control, vol. 63, no. 5, pp. 1329–1339, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  29. C. Xi and U. A. Khan, “DEXTRA: A fast algorithm for optimization over directed graphs,” IEEE Transactions on Automatic Control, vol. 62, no. 10, pp. 4980–4993, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  30. V. S. Mai and E. H. Abed, “Distributed optimization over weighted directed graphs using row stochastic matrix,” Proceedings of the American Control Conference, pp. 7165–7170, 2016.

  31. R. Xin, U. A. Khan, “A linear algorithm for optimization over directed graphs with geometric convergence,” IEEE Control Systems Letters, vol. 2, no. 3, pp. 235–330, 2018.

    Article  Google Scholar 

  32. C. Xi, V. S. Mai, E. H. Abed, and U. A. Khan, “Linear convergence in optimization over directed graphs with row-stochastic matrices,” IEEE Transactions on Automatic Control, vol. 63, no. 10, pp. 3558–3565, Oct. 2018.

    Article  MathSciNet  MATH  Google Scholar 

  33. Z. Wang and H. Li, “Edge-based stochastic gradient algorithm for distributed optimization,” IEEE Transactions on Network Science and Engineering, 2019. DOI: https://doi.org/10.1109/TNSE.2019.2933177

  34. A. Mokhtari and A. Ribeiro, “DSA: Decentralized double stochastic averaging gradient algorithm,” Journal of Machine Learning Research, vol. 17, pp. 1–35, 2016.

    MathSciNet  MATH  Google Scholar 

  35. L. An and G. Yang, “State estimation under sparse sensor attacks: A constrained set partitioning approach,” IEEE Transactions on Automatic Control, vol. 64, no. 9, pp. 3861–3868, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  36. H. Li, X. Liao, T. Huang, and W. Zhu, “Event-triggering sampling based leader-following consensus in second-order multi-agent systems,” IEEE Transactions on Automatic Control, vol. 60, no. 7, pp. 1998–2003, 2015.

    Article  MathSciNet  MATH  Google Scholar 

  37. H. Li, G. Chen, T. Huang, and Z. Dong, “Highperformance consensus control in networked systems with limited bandwidth communication and time-varying directed topologies,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 5, pp. 1043–1054, 2017.

    Article  Google Scholar 

  38. H. Lakshmanan and D. P. Farias, “Decentralized resource allocation in dynamic networks of agents,” SIAM Journal on Optimization, vol. 19, no. 2, pp. 911–940, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  39. V. Cevher, S. Becker, and M. Schmidt, “Convex optimization for big data: scalable, randomized, and parallel algorithms for big data analytics,” IEEE Signal Processing Magazine, vol. 31, no. 5, pp. 32–43, 2014.

    Article  Google Scholar 

  40. D. Yuan and D. W. C. Ho, “Randomized gradient-free method for multiagent optimization over time-varying networks,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 6, pp. 1342–1347, 2015.

    Article  MathSciNet  Google Scholar 

  41. C. Han and W. Wang, “Distributed observer-based LQ controller design and stabilization for discrete-time multiagent systems,” International Journal of Control, Automation, and Systems, vol. 16, no. 4, pp. 1765–1774, 2018.

    Article  MathSciNet  Google Scholar 

  42. G. Shi and K. H. Johansson, “Randomized optimal consensus of multiagent systems,” Automatica, vol. 48, no. 12, pp. 3018–3030, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  43. Y. Lou, G. Shi, K. H. Johansson, and Y. Hong, “Convergence of random sleep algorithms for optimal consensus,” Systems & Control Letters, vol. 62, no. 12, pp. 1196–1202, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  44. Y. Peng and Y. Hong, “Stochastic sub-gradient algorithm for distributed optimization with random sleep scheme,” Control Theory & Technology, vol. 13, no. 4, pp. 333–347, 2015.

    Article  MathSciNet  MATH  Google Scholar 

  45. A. Nedić, “Asynchronous broadcast-based convex optimization over a network,” IEEE Transactions on Automatic Control, vol. 56, no. 6, pp. 1337–1351, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  46. H. Li, Z. Wang, D. Xia and Q. Han, “Random sleep scheme-based distributed optimization algorithm over unbalanced time-varying networks,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019. DOI: https://doi.org/10.1109/TSMC.2019.2945864

  47. A. Makhdoumi and A. Ozdaglar, “Graph balancing for distributed subgradient methods over directed graphs,” Proc. of IEEE 54th Conf. Decision and Control, pp. 1364–1371, 2015.

  48. P. Xie, K. You, R. Tempo, S. Song, and C. Wu, “Distributed convex optimization with inequality constraints over time-varying unbalanced digraphs,” IEEE Transactions on Automatic Control, vol. 63, no. 12, pp. 4331–4337, Dec. 2018.

    Article  MathSciNet  MATH  Google Scholar 

  49. D. Blatt and A. Hero, “Energy-based sensor network source localization via projection onto convex sets,” IEEE Transactions on Signal Processing, vol. 54, no. 9, pp. 3614–3619, 2006.

    Article  MATH  Google Scholar 

  50. D. Dua and C. Graff, “UCI machine learning repository,” University of California, Irvine, School of Information and Computer Sciences. Available: https://archive.ics.uci.edu/ml/datasets/Mushroom.

Download references

Author information

Authors and Affiliations

  1. Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, P. R. China

    Zheng Wang, Lifeng Zheng & Huaqing Li

Authors
  1. Zheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lifeng Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huaqing Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Lifeng Zheng or Huaqing Li.

Additional information

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Wei He under the direction of Editor Fuchun Sun. The work described in this paper was supported in part by the Fundamental Research Funds for the Central Universities under Grant XDJK2019AC001, in part by the Innovation Support Program for Chongqing Overseas Returnees under Grant cx2019005, and in part by the National Natural Science Foundation of China under Grant 61773321, Grant 61673080.

Zheng Wang received his B.E. degree in Electronic Information Science and Technology from University of Jinan, China, in 2015, and an M.E. degree in Electronics and Communication Engineering from Southwest University, China, in 2018. His research interests include multi-agent systems and distributed optimization.

Lifeng Zheng Lifeng Zheng received his B.E. degree in internet of things engineering from Chongqing Three Gorges University, Chongqing, China, in 2017. He is currently working toward a master’s degree in the College of Electronic and Information Engineering, Southwest University, Chongqing, China. His research interests include networked system and distributed computing.

Huaqing Li received his B.S. degree in Information and Computing Science from Chongqing University of Posts and Telecommunications, in 2009, and a Ph.D. degree in Computer Science and Technology from Chongqing University in 2013. He was a Postdoctoral Researcher at School of Electrical and Information Engineering, The University of Sydney from Sept. 2014 to Sept. 2015, and at School of Electrical and Electronic Engineering, Nanyang Technological University from Nov. 2015 to Nov. 2016. From Jul. 2018, he has been a professor at College of Electronic and Information Engineering, Southwest University. His main research interests include nonlinear dynamics and control, multi-agent systems, and distributed optimization. He serves as a Regional Editor for Neural Computing & Applications and an Editorial Board Member for IEEE Access

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Z., Zheng, L. & Li, H. Distributed Optimization over General Directed Networks with Random Sleep Scheme. Int. J. Control Autom. Syst. 18, 2534–2542 (2020). https://doi.org/10.1007/s12555-018-9543-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-018-9543-9

Keywords

Search

Navigation