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Volume 9 Issue 10
Oct.  2022

IEEE/CAA Journal of Automatica Sinica

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X. Jiang, X. L. Zeng, J. Sun, J. Chen, and  Y. Wei,  “A fully distributed hybrid control framework for non-differentiable multi-agent optimization,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 10, pp. 1792–1800, Oct. 2022. doi: 10.1109/JAS.2022.105872
Citation: X. Jiang, X. L. Zeng, J. Sun, J. Chen, and  Y. Wei,  “A fully distributed hybrid control framework for non-differentiable multi-agent optimization,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 10, pp. 1792–1800, Oct. 2022. doi: 10.1109/JAS.2022.105872

A Fully Distributed Hybrid Control Framework For Non-Differentiable Multi-Agent Optimization

doi: 10.1109/JAS.2022.105872
Funds:  This work was supported in part by the National Key Research and Development Program of China (2021YFB1714800), the National Natural Science Foundation of China (61925303, 62088101, 62073035, 62173034) and the Natural Science Foundation of Chongqing (2021ZX4100027)
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  • This paper develops a fully distributed hybrid control framework for distributed constrained optimization problems. The individual cost functions are non-differentiable and convex. Based on hybrid dynamical systems, we present a distributed state-dependent hybrid design to improve the transient performance of distributed primal-dual first-order optimization methods. The proposed framework consists of a distributed constrained continuous-time mapping in the form of a differential inclusion and a distributed discrete-time mapping triggered by the satisfaction of local jump set. With the semistability theory of hybrid dynamical systems, the paper proves that the hybrid control algorithm converges to one optimal solution instead of oscillating among different solutions. Numerical simulations illustrate better transient performance of the proposed hybrid algorithm compared with the results of the existing continuous-time algorithms.

     

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    Highlights

    • This paper provides a fully distributed hybrid framework for solving the general large-scale constrained optimization problem, whose objective functions may be non-differentiable and non-strongly-convex. By introducing conflict-avoidance rule in the jump mapping, each agent in the network updates local variables by local information and transmitted information from neighbors. To our best knowledge, this is the first work studying fully distributed state-dependent hybrid methods for non-differentiable optimization problems
    • We provide complete and rigorous convergence proofs for the proposed distributed hybrid method with the invariance principle for hybrid dynamical systems. Because the objective function is non-strongly convex and non-differentiable, there may be a continuum of solutions to the optimization problem. With semi-stability theory, our proposed algorithm guarantees that the variables of different agents converge to one same optimal solution instead of oscillating among different solutions
    • This work has extended the existing hybrid works on consensus problems to distributed optimization problems. Compared with recent works for distributed optimization, the proposed fully distributed framework does not need a supervisory resetting and reduces the network communication burden. By numerical simulation, the proposed distributed hybrid algorithm shows an improved convergence performance than primal-dual continuous-time methods

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