Data-driven Polytopic Output Synchronization of Heterogeneous Multi-agent Systems from Noisy Data

TL;DR

This paper introduces a distributed data-driven control method for heterogeneous multi-agent systems that achieves near-optimal output synchronization despite noisy data, by using a polytopic representation and stability conditions formulated as semidefinite programs.

Contribution

It develops a novel noise-robust, data-driven control framework for output synchronization in heterogeneous MASs, incorporating a polytopic model and approximate solutions to regulator equations.

Findings

Achieves near-optimal synchronization with bounded error.

Handles noisy data effectively through polytopic representation.

Validated by numerical simulations demonstrating practical effectiveness.

Abstract

This paper proposes a novel approach to addressing the output synchronization problem in unknown heterogeneous multi-agent systems (MASs) using noisy data. Unlike existing studies that focus on noiseless data, we introduce a distributed data-driven controller that enables all heterogeneous followers to synchronize with a leader's trajectory. To handle the noise in the state-input-output data, we develop a data-based polytopic representation for the MAS. We tackle the issue of infeasibility in the set of output regulator equations caused by the noise by seeking approximate solutions via constrained fitting error minimization. This method utilizes measured data and a noise-matrix polytope to ensure near-optimal output synchronization. Stability conditions in the form of data-dependent semidefinite programs are derived, providing stabilizing controller gains for each follower. The proposed distributed data-driven control protocol achieves near-optimal output synchronization by ensuring the convergence of the tracking error to a bounded polytope, with the polytope size positively correlated with the noise bound. Numerical tests validate the practical merits of the proposed data-driven design and theory.