New data-driven control tames nonlinear systems under unknown periodic disturbances

Output regulation in nonlinear systems typically requires full model identification and solving regulator equations—a cumbersome process. A new arXiv preprint (Li et al., June 2026) sidesteps these steps entirely. The authors consider continuous-time nonlinear plants that are linearly parameterized over a nonlinear dictionary, with all coefficient matrices unknown. Instead of exact regulation, they pursue a frequency-selective objective: the steady-state error remains almost periodic, but its components at specific exosystem frequencies are forced to zero. A p-copy internal model is embedded into a dynamic controller, and the augmented system's unknown matrices are represented directly from measured data, eliminating the need for exosignal amplitude or phase measurement.

To design the controller, the team formulates a noise-robust semidefinite program that yields gains making the closed-loop vector field exponentially contractive on a prescribed operating set. This guarantees a unique, bounded, and attracting steady-state trajectory. Using contraction theory and Fourier-Bohr analysis, they prove the trajectory is almost periodic, the targeted frequency components vanish, and the unmodeled spectral energy satisfies a Parseval-type bound. Numerical and physics-based simulations on a quadrotor carrying a cable-suspended payload demonstrate the method's robustness and effectiveness, offering a practical path for controlling drones and industrial systems under unknown periodic disturbances without extensive modeling.