Sparse Network Optimization for Synchronization

نویسندگان

چکیده

We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of adjacency matrix graph and coupling strength network, modelling so-called coupled oscillators. Besides sparsity, we aim to obtain graphs which have good connectivity properties, resulting small formulate three this purpose. Our first model a mixed integer problem, subject ODE constraints, reminiscent an optimal control problem. As expected, problem computationally very challenging, if not impossible, solve, only because it involves binary variables but also some its are functions. second continuous relaxation one, third discretization second, tractable by employing standard software. design synchronize, solving relaxed applying practical algorithm various sizes, with randomly generated intrinsic natural frequencies initial phase variables. test robustness these carrying out numerical simulations random data constructing expected value network’s order parameter variance under data, as guide assessment.

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ژورنال

عنوان ژورنال: Journal of Optimization Theory and Applications

سال: 2021

ISSN: ['0022-3239', '1573-2878']

DOI: https://doi.org/10.1007/s10957-021-01933-9