Adaptive Disturbance Learning for Constrained Systems: A HOPF-Oscillator Driven Tube-MPC Approach

This paper investigates the robust control problem for constrained systems subject to unknown multi-harmonic disturbances. We propose a composite control approach that integrates a Hopf-oscillator-based learning module with Tubebased Model Predictive Control (Tube-MPC). The core innovation lies in addressing the inherent conflict between learninginduced transients and system safety: while the adaptive oscillators learning disturbance features online, the Tube-MPC provides a robust positively invariant (RPI) safety buffer that effectively absorbs oscillatory and non-monotonic learning residuals. By incorporating the learned disturbance into a feedforward compensation term, the proposed method reduces the effective disturbance impact acting on the plant, thereby enhancing steady-state accuracy and reducing control effort. Theoretical analysis and simulation results confirm that the approach guarantees recursive feasibility and hard-constraint satisfaction throughout the adaptive learning process.