# A Distributed Adaptive Scheme for Multi-Agent Systems

## TL;DR

This paper introduces a novel distributed adaptive control scheme for multi-agent systems that achieves asymptotic consensus without relying on the gradient of Lyapunov functions, addressing limitations of traditional adaptive control in distributed settings.

## Contribution

It proposes a new adaptive scheme that works for general multi-agent systems and does not depend on gradient-based Lyapunov functions, enabling distributed implementation.

## Key findings

- Achieves asymptotic consensus in second-order uncertain multi-agent systems.
- Works on directed graph networks.
- Does not rely on gradient of Lyapunov functions.

## Abstract

In traditional adaptive control, the certainty equivalence principle suggests a two-step design scheme. A controller is first designed for the ideal situation assuming the uncertain parameter was known and it renders a Lyapunov function. Then, the uncertain parameter in the controller is replaced by its estimation that is updated by an adaptive law along the gradient of Lyapunov function. This principle does not generally work for a multi-agent system as an adaptive law based on the gradient of (centrally constructed) Lyapunov function cannot be implemented in a distributed fashion, except for limited situations. In this paper, we propose a novel distributed adaptive scheme, not relying on gradient of Lyapunov function, for general multi-agent systems. In this scheme, asymptotic consensus of a second-order uncertain multi-agent system is achieved in a network of directed graph.