# Optimal Output Consensus of High-Order Multi-Agent Systems with Embedded Technique

## TL;DR

This paper presents a novel embedded control approach for achieving optimal output consensus in high-order multi-agent systems with multi-input multi-output dynamics, ensuring convergence to the global cost function's optimum.

## Contribution

It introduces an optimal signal generator and embedded control schemes for high-order agents, extending output consensus to include optimization objectives.

## Key findings

- Algorithms guarantee consensus on the optimal solution.
- Embedded technique ensures solvability under standard assumptions.
- Applicable to high-order multi-input multi-output systems.

## Abstract

In this paper, we study an optimal output consensus problem for a multi-agent network with agents in the form of multi-input multi-output minimum-phase dynamics. Optimal output consensus can be taken as an extended version of the existing output consensus problem for higher-order agents with an optimization requirement, where the output variables of agents are driven to achieve a consensus on the optimal solution of a global cost function. To solve this problem, we first construct an optimal signal generator, and then propose an embedded control scheme by embedding the generator in the feedback loop. We give two kinds of algorithms based on different available information along with both state feedback and output feedback, and prove that these algorithms with the embedded technique can guarantee the solvability of the problem for high-order multi-agent systems under standard assumptions.