We numerically explore data-driven cluster-based control of a noisy Van der Pol oscillator, with the aim of elucidating the underlying feedback suppression mechanisms. The controller behavior is examined under three distinct conditions: a deterministic oscillator, an oscillator perturbed by additive white Gaussian noise, and an oscillator perturbed by correlated disturbances modeled by Ornstein–Uhlenbeck colored noise. Across all cases, we find that cluster-based actuation suppresses self-excited oscillations by reshaping the phase-space dynamics and steering the trajectories toward a stable equilibrium. Analysis of the cluster transitions reveals that this quenching is achieved by interrupting the natural limit-cycle progression at a small number of strategic switching clusters, a mechanism that persists even under substantial stochastic disturbances. The influence of a cost penalization parameter is further examined, revealing distinct regimes that balance oscillation suppression against actuation effort. These results provide mechanistic insight and practical guidance for the application of data-driven, model-free cluster-based control to nonlinear self-excited systems.

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• Control theory
• Instability control
• Noise
• Stochastic processes