New PRPC method reduces prediction error in data-driven control

Indirect data-driven predictive control often struggles with process noise and limited data. The new Projection-Regularized Predictive Control (PRPC), proposed by Mahmood Mazare and Hossein Ramezani (arXiv:2607.28123), keeps the fundamental-lemma weight vector but adds a regularized projection. This projection is analytically condensed into a fixed-dimension covariance update, making the algorithm efficient and practical for real-time use. A rigorous bias-variance analysis proves PRPC strictly lowers prediction error compared to unregularized subspace methods, particularly under errors-in-variables conditions and structural rank deficiencies.

PRPC is extended to an adaptive sliding-window controller for linear time-varying (LTV) systems. To ensure safety despite closed-loop data correlations, the authors derive a uniform-in-time, finite-sample confidence bound using vector-valued martingale concentration inequalities. This uncertainty radius is embedded into a dynamically tightened constraint set, guaranteeing robust recursive feasibility and Input-to-State practical Stability (ISpS) with high probability. Simulations on both LTI and LTV benchmarks confirm real-time tractability and strict constraint satisfaction, positioning PRPC as a robust alternative for safety-critical data-driven control applications.