# Input-Feedforward-Passivity-Based Distributed Optimization Over Jointly Connected Balanced Digraphs

## TL;DR

This paper introduces a novel passivity-based distributed optimization algorithm for directed graphs, ensuring exponential convergence without global information, and demonstrates its effectiveness through numerical examples.

## Contribution

It proposes a new input feedforward passivity framework and a derivative feedback algorithm that work over directed, weight-balanced graphs without requiring eigenvalue knowledge.

## Key findings

- The algorithm guarantees exponential convergence on strongly connected topologies.
- It is robust to randomly changing weight-balanced digraphs.
- Numerical examples validate the effectiveness of the proposed methods.

## Abstract

In this paper, a distributed optimization problem is investigated via input feedforward passivity. First, an input-feedforward-passivity-based continuous-time distributed algorithm is proposed. It is shown that the error system of the proposed algorithm can be decomposed into a group of individual input feedforward passive (IFP) systems that interact with each other using output feedback information. Based on this IFP framework, convergence conditions of a suitable coupling gain are derived over weight-balanced and uniformly jointly strongly connected (UJSC) topologies. It is also shown that the IFP-based algorithm converges exponentially when the topology is strongly connected. Second, a novel distributed derivative feedback algorithm is proposed based on the passivation of IFP systems. While most works on directed topologies require knowledge of eigenvalues of the graph Laplacian, the derivative feedback algorithm is fully distributed, namely, it is robust against randomly changing weight-balanced digraphs with any positive coupling gain and without knowing any global information. Finally, numerical examples are presented to illustrate the proposed distributed algorithms.