# The Cooperative Output Regulation Problem of Discrete-Time Linear Multi-Agent Systems by the Adaptive Distributed Observer

## TL;DR

This paper introduces an adaptive distributed observer for discrete-time linear multi-agent systems, enabling followers to estimate leader signals and system matrices, and proposes control laws to solve the cooperative output regulation problem.

## Contribution

It develops a novel adaptive distributed observer that estimates both leader signals and system matrices, facilitating a new solution to the cooperative output regulation problem.

## Key findings

- Successful estimation of leader signals and system matrices by followers.
- Effective discrete adaptive algorithms for regulator equations.
- Achievement of cooperative output regulation using proposed control laws.

## Abstract

In this paper, we first present an adaptive distributed observer for a discrete-time leader system. This adaptive distributed observer will provide, to each follower, not only the estimation of the leader's signal, but also the estimation of the leader's system matrix. Then, based on the estimation of the matrix S, we devise a discrete adaptive algorithm to calculate the solution to the regulator equations associated with each follower, and obtain an estimated feedforward control gain. Finally, we solve the cooperative output regulation problem for discrete-time linear multi-agent systems by both state feedback and output feedback adaptive distributed control laws utilizing the adaptive distributed observer.