# Distributed Optimization for a Class of High-order Nonlinear Multi-agent Systems with Unknown Dynamics

## TL;DR

This paper develops distributed adaptive control algorithms for high-order nonlinear multi-agent systems with unknown dynamics, enabling agents to collaboratively reach the global optimum despite nonlinear uncertainties.

## Contribution

It introduces a novel embedded control design and adaptive controllers for high-order nonlinear agents, addressing unknown dynamics in distributed optimization.

## Key findings

- Agents' outputs converge to the global optimal solution.
- Estimated parameters converge to true values under persistence of excitation.
- Algorithms are validated through simulation examples.

## Abstract

In this paper, we study a distributed optimization problem for a class of high-order multi-agent systems with unknown dynamics. In comparison with existing results for integrators or linear agents, we need to overcome the difficulties brought by the unknown nonlinearities and also the optimization requirement. For this purpose, we employ an embedded control based design and first convert this problem into an output stabilization problem. Then, two kinds of adaptive controllers are given for these agents to drive their outputs to the global optimal solution under some mild conditions. Finally, we show that the estimated parameter vector converges to the true parameter vector under some well-known persistence of excitation condition. The efficacy of these algorithms was verified by a simulation example.