Scalable Nonlinear DeePC: Bridging Direct and Indirect Methods and Basis Reduction

Abstract: This paper studies regularized data-enabled predictive control (DeePC) within a nonlinear framework and its relationship to subspace predictive control (SPC). The $Π$-regularization is extended to general basis functions and it is shown that, under suitable conditions, the resulting basis functions DeePC formulation constitutes a relaxation of basis functions SPC. To improve scalability, we introduce an SVD-based dimensionality reduction that preserves the equivalence with SPC, and we derive a reduced Π-regularization. A LASSO based sparse basis selection method is proposed to obtain a reduced basis from lifted data. Simulations on a nonlinear van der Pol oscillator model indicate that, in the absence of noise, DeePC and SPC yield equivalent absolute mean tracking errors (AMEs) when large penalties are applied. In contrast, under noisy measurements, careful tuning of the DeePC regularization results in a reduced AME, outperforming SPC.