## Samenvatting

A new approach to distributed consensus optimization is studied in this paper. The cost function to be minimized is a sum of local cost functions which are not

necessarily convex as long as their sum is convex. This benefit is obtained from a recent observation that, with a large gain in the diffusive coupling, heterogeneous multi-agent systems behave like a single dynamical system whose vector field is simply the average of all agents’ vector fields. However, design

of the large coupling gain requires global information such as network structure and individual agent dynamics. In this paper, we employ a nonlinear time-varying coupling of diffusive type, which we call ‘edge-wise funnel coupling.’ This idea is

borrowed from adaptive control, which enables decentralized design of distributed optimizers without knowledge of global information. Remarkably, without a common internal model, each agent achieves asymptotic consensus to the optimal solution of the global cost. We illustrate this result by a network

that asymptotically finds the least-squares solution of a linear

equation in a distributed manner.

necessarily convex as long as their sum is convex. This benefit is obtained from a recent observation that, with a large gain in the diffusive coupling, heterogeneous multi-agent systems behave like a single dynamical system whose vector field is simply the average of all agents’ vector fields. However, design

of the large coupling gain requires global information such as network structure and individual agent dynamics. In this paper, we employ a nonlinear time-varying coupling of diffusive type, which we call ‘edge-wise funnel coupling.’ This idea is

borrowed from adaptive control, which enables decentralized design of distributed optimizers without knowledge of global information. Remarkably, without a common internal model, each agent achieves asymptotic consensus to the optimal solution of the global cost. We illustrate this result by a network

that asymptotically finds the least-squares solution of a linear

equation in a distributed manner.

Originele taal-2 | English |
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Titel | Proceeding of ECC 2020 |

Uitgeverij | EUKA |

Pagina's | 911-916 |

Aantal pagina's | 6 |

Status | Published - mei-2020 |

Evenement | 2020 European Control Conference (ECC) - Saint Petersburg, Russian Federation Duur: 12-mei-2020 → 15-mei-2020 |

### Conference

Conference | 2020 European Control Conference (ECC) |
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Land/Regio | Russian Federation |

Stad | Saint Petersburg |

Periode | 12/05/2020 → 15/05/2020 |