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Volume 8 Issue 9
Sep.  2021

IEEE/CAA Journal of Automatica Sinica

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W.-T. Lin, Y.-W. Wang, C. J. Li, and X. H. Yu, "Distributed Resource Allocation via Accelerated Saddle Point Dynamics," IEEE/CAA J. Autom. Sinica, vol. 8, no. 9, pp. 1588-1599, Sep. 2021. doi: 10.1109/JAS.2021.1004114
Citation: W.-T. Lin, Y.-W. Wang, C. J. Li, and X. H. Yu, "Distributed Resource Allocation via Accelerated Saddle Point Dynamics," IEEE/CAA J. Autom. Sinica, vol. 8, no. 9, pp. 1588-1599, Sep. 2021. doi: 10.1109/JAS.2021.1004114

Distributed Resource Allocation via Accelerated Saddle Point Dynamics

doi: 10.1109/JAS.2021.1004114
Funds:  This work was supported by the National Natural Science Foundation of China (61773172) and supported in part by the Australian Research Council (DP200101197, DE210100274)
More Information
  • In this paper, accelerated saddle point dynamics is proposed for distributed resource allocation over a multi-agent network, which enables a hyper-exponential convergence rate. Specifically, an inertial fast-slow dynamical system with vanishing damping is introduced, based on which the distributed saddle point algorithm is designed. The dual variables are updated in two time scales, i.e., the fast manifold and the slow manifold. In the fast manifold, the consensus of the Lagrangian multipliers and the tracking of the constraints are pursued by the consensus protocol. In the slow manifold, the updating of the Lagrangian multipliers is accelerated by inertial terms. Hyper-exponential stability is defined to characterize a faster convergence of our proposed algorithm in comparison with conventional primal-dual algorithms for distributed resource allocation. The simulation of the application in the energy dispatch problem verifies the result, which demonstrates the fast convergence of the proposed saddle point dynamics.


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  • [1]
    K. Li, Q. Liu, S. Yang, J. Cao, and G. Lu, “Cooperative optimization of dual multiagent system for optimal resource allocation,” IEEE Trans. Systems,Man,and Cybernetics:Systems, vol. 50, no. 11, pp. 4676–4687, 2018.
    C. Li, X. Yu, W. Yu, T. Huang, and Z. W. Liu, “Distributed eventtriggered scheme for economic dispatch in smart grids,” IEEE Trans. Industrial Informatics, vol. 12, no. 5, pp. 1775–1785, 2016. doi: 10.1109/TII.2015.2479558
    S. Bolognani, R. Carli, G. Cavraro, and S. Zampieri, “Distributed reactive power feedback control for voltage regulation and loss minimization,” IEEE Trans. Automatic Control, vol. 60, no. 4, pp. 966–981, 2013.
    Y. Zhang and G. B. Giannakis, “Distributed stochastic market clearing with high-penetration wind power,” IEEE Trans. Power Systems, vol. 31, no. 2, pp. 895–906, 2015.
    B. Baingana, G. Mateos, and G. B. Giannakis, “Proximal-gradient algorithms for tracking cascades over social networks,” IEEE Journal of Selected Topics in Signal Processing, vol. 8, no. 4, pp. 563–575, 2014. doi: 10.1109/JSTSP.2014.2317284
    G. Mateos and G. B. Giannakis, “Distributed recursive least-squares: Stability and performance analysis,” IEEE Trans. Signal Processing, vol. 60, no. 7, pp. 3740–3754, 2011.
    V. Lesser, C. L. O. Jr, and M. Tambe, Distributed Sensor Networks. New York, US: Springer, 2003.
    S. Martinez, F. Bullo, J. Cortes, and E. Frazzoli, “On synchronous robotic networksłpart i: Models, tasks, and complexity,” IEEE Trans. Automatic Control, vol. 52, no. 12, pp. 2199–2213, 2007. doi: 10.1109/TAC.2007.908301
    L. Ding, Q.-L. Han, L. Y. Wang, and E. Sindi, “Distributed cooperative optimal control of dc microgrids with communication delays,” IEEE Trans. Industrial Informatics, vol. 14, no. 9, pp. 3924–3935, 2018. doi: 10.1109/TII.2018.2799239
    H. Halabian, “Distributed resource allocation optimization in 5G virtualized networks,” IEEE Journal on Selected Areas in Communications, vol. 37, no. 3, pp. 627–642, 2019. doi: 10.1109/JSAC.2019.2894305
    Z. Chang, Z. Wang, X. Guo, C. Yang, Z. Han, and T. Ristaniemi, “Distributed resource allocation for energy efficiency in ofdma multicell networks with wireless power transfer,” IEEE Journal on Selected Areas in Communications, vol. 37, no. 2, pp. 345–356, 2018.
    C. Long, J. Wu, C. Zhang, L. Thomas, M. Cheng, and N. Jenkins, “Peerto-peer energy trading in a community microgrid,” in Proc. IEEE Power & Energy Society General Meeting, 2017, pp. 1–5.
    R. Xie, F. R. Yu, and H. Ji, “Dynamic resource allocation for heterogeneous services in cognitive radio networks with imperfect channel sensing,” IEEE Trans. Vehicular Technology, vol. 61, no. 2, pp. 770–780, 2011.
    C. Xu and X. He, “A fully distributed approach to optimal energy scheduling of users and generators considering a novel combined neurodynamic algorithm in smart grid,” IEEE/CAA Journal of Automatica Sinica, vol. 8, no. 7, pp. 1325–1335, 2020.
    Q. Dong, L. Yu, W. Song, J. Yang, Y. Wu, and J. Qi, “Fast distributed demand response algorithm in smart grid,” IEEE/CAA Journal of Automatica Sinica, vol. 4, no. 2, pp. 280–296, 2017. doi: 10.1109/JAS.2017.7510529
    G. Chen and E. Feng, “Distributed secondary control and optimal power sharing in microgrids,” IEEE/CAA Journal of Automatica Sinica, vol. 2, no. 3, pp. 304–312, 2015. doi: 10.1109/JAS.2015.7152665
    A. Nedic, A. Ozdaglar, and P. A. Parrilo, “Constrained consensus and optimization in multi-agent networks,” IEEE Trans. Automatic Control, vol. 55, no. 4, pp. 922–938, 2010. doi: 10.1109/TAC.2010.2041686
    M. Zhu and S. Martinez, “On distributed convex optimization under inequality and equality constraints,” IEEE Trans. Automatic Control, vol. 57, no. 1, pp. 151–164, 2011.
    S. Liang, X. Zeng, and Y. Hong, “Distributed nonsmooth optimization with coupled inequality constraints via modified lagrangian function,” IEEE Trans. Automatic Control, vol. 63, no. 6, pp. 1753–1759, 2017.
    P. Yi, Y. Hong, and F. Liu, “Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems,” Automatica, vol. 74, pp. 259–269, 2016. doi: 10.1016/j.automatica.2016.08.007
    X. Le, S. Chen, Z. Yan, and J. Xi, “A neurodynamic approach to distributed optimization with globally coupled constraints,” IEEE Trans. Cybernetics, vol. 48, no. 11, pp. 3149–3158, 2017.
    C. Li, X. Yu, T. Huang, and X. He, “Distributed optimal consensus over resource allocation network and its application to dynamical economic dispatch,” IEEE Trans. Neural Networks &Learning Systems, vol. 29, no. 6, pp. 2407–2418, 2017.
    X. He, D. W. C. Ho, T. Huang, J. Yu, H. Abu-Rub, and C. Li, “Second order continuous-time algorithms for economic power dispatch in smart grids,” IEEE Trans. Systems Man &Cybernetics Systems, vol. 48, no. 9, pp. 1482–1492, 2017.
    J. Cortes and S. K. Niéderländer, “Distributed coordination for non-smooth convex optimization via saddle-point dynamics,” Journal of Nonlinear Science, vol. 29, no. 4, pp. 1247–1272, 2019.
    L. Bai, M. Ye, C. Sun, and G. Hu, “Distributed economic dispatch control via saddle point dynamics and consensus algorithms,” IEEE Trans. Control Systems Technology, vol. 27, no. 2, pp. 898–905, 2017.
    Z. Deng, S. Liang, and Y. Hong, “Distributed continuous-time algorithms for resource allocation problems over weight-balanced digraphs,” IEEE Trans. Cybernetics, vol. 48, no. 11, pp. 3116–3125, 2017.
    G. Qu and N. Li, “Accelerated distributed nesterov gradient descent,” IEEE Trans. Automatic Control, vol. 65, no. 6, pp. 2566–2581, 2020. doi: 10.1109/TAC.2019.2937496
    C. Li, X. Yu, X. Zhou, and W. Ren, “A fixed time distributed optimization: A sliding mode perspective,” in Proc. 43rd Annual Conf. IEEE Industrial Electronics Society, 2017, pp. 8201–8207.
    G. Chen and Z. Li, “A fixed-time convergent algorithm for distributed convex optimization in multi-agent systems,” Automatica, vol. 95, pp. 539–543, 2018.
    H. K. Khalil, “Nonlinear systems third edition,” Upper Saddle River, NJ: Prentice-Hall, Inc., 2002.
    R. A. Freeman, P. Yang, and K. M. Lynch, “Stability and convergence properties of dynamic average consensus estimators,” in Proc. 45th IEEE Conf. Decision and Control, 2006, pp. 338–343.
    W. Ren, “Multivehicle consensus with a time-varying reference state,” Systems &Control Letters, vol. 56, no. 7, pp. 474–483, 2007.
    W. Su, S. Boyd, and E. Candes, “A differential equation for modeling nesterovs accelerated gradient method: Theory and insights,” in Proc. Advances Neural Information Processing Systems, 2014, pp. 2510–2518.
    A. Cherukuri, B. Gharesifard, and J. Cortes, “Saddle-point dynamics: conditions for asymptotic stability of saddle points,” Siam Journal on Control &Optimization, vol. 2015, no. 1, pp. 2020–2025, 2017.
    G. Qu and N. Li, “On the exponential stability of primal-dual gradient dynamics,” IEEE Control Systems Letters, vol. 3, no. 1, pp. 43–48, 2019. doi: 10.1109/LCSYS.2018.2851375


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    • Accelerated saddle point dynamics are firstly proposed for resource allocation.
    • The proposed algorithm is initialization-free.
    • An inertial fast-slow dynamical system is introduced for distributed algorithm design.


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