  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.
