# Distributed Coordination for a Class of Nonlinear Multi-agent Systems with Regulation Constraints

## TL;DR

This paper develops a passivity-based distributed control method for nonlinear multi-agent systems to achieve optimal steady-state regulation under noisy data and without a leader, extending existing approaches.

## Contribution

It introduces a novel distributed optimization approach that handles regulation constraints and noisy observations for nonlinear agents without relying on a leader.

## Key findings

- Achieves optimal steady-state regulation despite observation noise.
- Ensures convergence for passive nonlinear multi-agent systems.
- Validated effectiveness through applications and simulations.

## Abstract

In this paper, a multi-agent coordination problem with steady-state regulation constraints is investigated for a class of nonlinear systems. Unlike existing leader-following coordination formulations, the reference signal is not given by a dynamic autonomous leader but determined as the optimal solution of a distributed optimization problem. Furthermore, we consider a global constraint having noisy data observations for the optimization problem, which implies that reference signal is not trivially available with existing optimization algorithms. To handle those challenges, we present a passivity-based analysis and design approach by using only local objective function, local data observation and exchanged information from their neighbors. The proposed distributed algorithms are shown to achieve the optimal steady-state regulation by rejecting the unknown observation disturbances for passive nonlinear agents, which are persuasive in various practical problems. Applications and simulation examples are then given to verify the effectiveness of our design.