Skip to main content
SpringerLink
Log in

Distributed resource allocation: an indirect dual ascent method with an exponential convergence rate

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, an indirect dual ascent method with an exponential convergence rate is proposed for a general resource allocation problem with convex objectives and weighted constraints. By introducing the indirect dual variables, the dual dynamics can be executed in a decentralized manner by all nodes over the network. In contrast to the conventional methods, consensus on all the dual variables is not required. This further leads to the fast convergence, reduced communication burden and better privacy preserving. Moreover, the exponential convergence rate of the proposed algorithm is established through the Lyapunov method and the singular perturbation theory. Application of the dynamic power dispatch problem in smart grid verifies the effectiveness and performance of the proposed algorithm.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Li, C., Yu, X., Yu, W., Huang, T., Liu, Z.W.: Distributed event-triggered scheme for economic dispatch in smart grids. IEEE Trans. Ind. Inform. 12(5), 1775–1785 (2016)

    Article  Google Scholar 

  2. Li, C., Yan, X., Xinghuo, Y., Ryan, C., Huang, T.: Risk-averse energy trading in multienergy microgrids: a two-stage stochastic game approach. IEEE Trans. Ind. Inform. 13(5), 2620–2630 (2017)

    Article  Google Scholar 

  3. Li, C., Liu, C., Deng, K., Xinghuo, Y., Huang, T.: Data-driven charging strategy of pevs under transformer aging risk. IEEE Trans. Control Syst. Technol. 26(4), 1386–1399 (2017)

    Article  Google Scholar 

  4. Baingana, B., Mateos, G., Giannakis, G.B.: Proximal-gradient algorithms for tracking cascades over social networks. IEEE J. Sel. Topics Signal Process. 8(4), 563–575 (2014)

    Article  Google Scholar 

  5. Mateos, G., Giannakis, G.B.: Distributed recursive least-squares: stability and performance analysis. IEEE Trans. Signal Process. 60(7), 3740–3754 (2011)

    Article  MathSciNet  Google Scholar 

  6. Lesser, V., Ortiz Jr., C.L., Tambe, M.: Distributed Sensor Networks. Springer, New York (2003)

    Book  Google Scholar 

  7. Martinez, S., Bullo, F., Cortes, J., Frazzoli, E.: On synchronous robotic networkspart i: models, tasks, and complexity. IEEE Trans. Autom. Control 52(12), 2199–2213 (2007)

    Article  Google Scholar 

  8. Wang, H., Liao, X., Huang, T.: Accelerated consensus to accurate average in multi-agent networks via state prediction. Nonlinear Dynamics 73(1–2), 551–563 (2013)

    Article  MathSciNet  Google Scholar 

  9. Huang, Y., Jia, Y.: Fixed-time consensus tracking control of second-order multi-agent systems with inherent nonlinear dynamics via output feedback. Nonlinear Dynamics 91(2), 1289–1306 (2018)

    Article  Google Scholar 

  10. Liu, X., Ho, D.W.C., Song, Q., Cao, J.: Finite-/fixed-time robust stabilization of switched discontinuous systems with disturbances. Nonlinear Dynamics 90(3), 2057–2068 (2017)

    Article  MathSciNet  Google Scholar 

  11. Nedić, A., Ozdaglar, A., Parrilo, P.A.: Constrained consensus and optimization in multi-agent networks. IEEE Trans. Autom. Control 55(4), 922–938 (2010)

    Article  MathSciNet  Google Scholar 

  12. Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J., et al.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)

    Article  Google Scholar 

  13. Duchi, J.C., Agarwal, A., Wainwright, M.J.: Dual averaging for distributed optimization: convergence analysis and network scaling. IEEE Trans. Autom. Control 57(3), 592–606 (2011)

    Article  MathSciNet  Google Scholar 

  14. Johansson, B., Rabi, M., Johansson, M.: A randomized incremental subgradient method for distributed optimization in networked systems. SIAM J. Optim. 20(3), 1157–1170 (2009)

    Article  MathSciNet  Google Scholar 

  15. Nedic, A., Ozdaglar, A.: Distributed subgradient methods for multi-agent optimization. IEEE Trans. Autom. Control 54(1), 48 (2009)

    Article  MathSciNet  Google Scholar 

  16. Zhu, M., Martínez, S.: On distributed convex optimization under inequality and equality constraints. IEEE Trans. Autom. Control 57(1), 151–164 (2011)

    MathSciNet  MATH  Google Scholar 

  17. Wang, X.-Y., Song, J.-M.: Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control. Commun. Nonlinear Sci. Numer. Simul. 14(8), 3351–3357 (2009)

    Article  Google Scholar 

  18. Wang, X., He, Y.: Projective synchronization of fractional order chaotic system based on linear separation. Phys. Lett. A 372(4), 435–441 (2008)

    Article  Google Scholar 

  19. Wang, X., Wang, M.: Dynamic analysis of the fractional-order Liu system and its synchronization. Chaos Interdiscip. J. Nonlinear Sci. 17(3), 033106 (2007)

    Article  Google Scholar 

  20. Wang, Y., Zhang, H., Wang, X., Yang, D.: Networked synchronization control of coupled dynamic networks with time-varying delay. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 40(6), 1468–1479 (2010)

    Article  Google Scholar 

  21. Zhang, H., Wang, X.-Y., Lin, X.-H.: Topology identification and module-phase synchronization of neural network with time delay. IEEE Trans. Syst. Man Cybern. Syst. 47(6), 885–892 (2016)

    Article  Google Scholar 

  22. Azin, H., Mohammadi, F., Machado, J.A.T.: A piecewise spectral-collocation method for solving fractional Riccati differential equation in large domains. Comput. Appl. Math. 38(3), 96 (2019)

    Article  MathSciNet  Google Scholar 

  23. Pahnehkolaei, S.M.A., Alfi, A., Machado, J.A.T.: Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with quad condition. Appl. Math. Comput. 359, 278–293 (2019)

    MathSciNet  MATH  Google Scholar 

  24. Moghaddam, B.P., Dabiri, A., Lopes, A.M., Machado, J.A.T.: Numerical solution of mixed-type fractional functional differential equations using modified Lucas polynomials. Comput. Appl. Math. 38(2), 46 (2019)

    Article  MathSciNet  Google Scholar 

  25. Kia, S.S., Cortés, J., Martínez, S.: Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication. Automatica 55, 254–264 (2015)

    Article  MathSciNet  Google Scholar 

  26. Gharesifard, B., Cortés, J.: Distributed continuous-time convex optimization on weight-balanced digraphs. IEEE Trans. Autom. Control 59(3), 781–786 (2014)

    Article  MathSciNet  Google Scholar 

  27. Yi, P., Hong, Y., Liu, F.: Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems. Automatica 74, 259–269 (2016)

    Article  MathSciNet  Google Scholar 

  28. Deng, Z., Liang, S., Hong, Y.: Distributed continuous-time algorithms for resource allocation problems over weight-balanced digraphs. IEEE Trans. Cybern. 99, 1–10 (2017)

    Google Scholar 

  29. Li, C., Yu, X., Huang, T., He, X.: Distributed optimal consensus over resource allocation network and its application to dynamical economic dispatch. IEEE Trans. Neural Netw. Learn. Syst. 29, 1–12 (2017)

    Google Scholar 

  30. He, X., Ho, D.W.C., Huang, T., Yu, J., Abu-Rub, H., Li, C.: Second-order continuous-time algorithms for economic power dispatch in smart grids. IEEE Trans. Syst. Man Cybern. Syst. 48(9), 1482–1492 (2018)

    Article  Google Scholar 

  31. Bai, L., Ye, M., Sun, C., Hu, G.: Distributed economic dispatch control via saddle point dynamics and consensus algorithms. IEEE Trans. Control Syst. Technol. 27, 1–8 (2017)

    Google Scholar 

  32. Zhu, M., Martinez, Sonia: On distributed convex optimization under inequality and equality constraints. IEEE Trans. Autom. Control 57(1), 151–164 (2011)

    MathSciNet  MATH  Google Scholar 

  33. Le, X., Chen, S., Yan, Z., Xi, J.: A neurodynamic approach to distributed optimization with globally coupled constraints. IEEE Trans. Cybern. 99, 1–10 (2017)

    Google Scholar 

  34. Cherukuri, A., Mallada, E., Cortés, J.: Asymptotic convergence of constrained primal-dual dynamics. Syst. Control Lett. 87, 10–15 (2016)

    Article  MathSciNet  Google Scholar 

  35. Cherukuri, A., Mallada, E., Low, S., Cortés, J.: The role of convexity in saddle-point dynamics: Lyapunov function and robustness. IEEE Trans. Autom. Control 63(8), 2449–2464 (2018)

    Article  MathSciNet  Google Scholar 

  36. Cortés, J., Niederländer, S.K.: Distributed coordination for nonsmooth convex optimization via saddle-point dynamics. J. Nonlinear Sci. 29, 1–26 (2018)

    MathSciNet  MATH  Google Scholar 

  37. Guannan, Q., Li, N.: On the exponential stability of primal-dual gradient dynamics. IEEE Control Syst. Lett. 3(1), 43–48 (2018)

    Google Scholar 

  38. Kia, S.S., Cortés, J., Martinez, S.: Dynamic average consensus under limited control authority and privacy requirements. Int. J. Robust Nonlinear Control 25(13), 1941–1966 (2015)

    Article  MathSciNet  Google Scholar 

  39. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)

    Book  Google Scholar 

  40. Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice-Hall Inc., Upper Saddle River (2002)

    MATH  Google Scholar 

  41. IEEE 30-Bus Test Case. https://www.ee.washington.edu/research/pstca/pf30/pg_tca30bus.htm/ (1961). Accessed 31 Dec 1961

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grants 61773172, 61572210 and 51537003, the Natural Science Foundation of Hubei Province of China (2017CFA035), the Fundamental Research Funds for the Central Universities (2018KFYYX-JJ119), the Program for HUST Academic Frontier Youth Team and the 111 Project on Computational Intelligence and Intelligent Control under Grant B18024 and the Australian Research Council under Grant DP170102303.

Author information

Authors and Affiliations

  1. School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, 430074, China

    Wen-Ting Lin & Yan-Wu Wang

  2. Key Laboratory of Image Processing and Intelligent Control (Huazhong University of Science and Technology), Ministry of Education, Wuhan, China

    Wen-Ting Lin & Yan-Wu Wang

  3. School of Electrical Engineering and Telecommunications, UNSW, Kingston, NSW 2052, Australia

    Chaojie Li

  4. School of Engineering, RMIT University, Melbourne, VIC, 3000, Australia

    Xinghuo Yu

Authors
  1. Wen-Ting Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yan-Wu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chaojie Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xinghuo Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan-Wu Wang.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Submitted to Nonlinear Dynamics, May 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, WT., Wang, YW., Li, C. et al. Distributed resource allocation: an indirect dual ascent method with an exponential convergence rate. Nonlinear Dyn 102, 1685–1699 (2020). https://doi.org/10.1007/s11071-019-05376-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-019-05376-w

Keywords

Search

Navigation