Projection-Regularized Indirect Data-Driven Predictive Control

Indirect data-driven predictive control methods often suffer under process noise and data scarcity. This paper introduces Projection-Regularized Predictive Control (PRPC), retaining the fundamental-lemma weight vector via a regularized projection analytically condensed into an efficient, fixed-dimension covariance update. A rigorous bias--variance analysis proves PRPC strictly reduces prediction error under process noise (errors-in-variables) and structural rank deficiencies compared to unregularized subspace methods. We leverage these properties to develop an adaptive sliding-window controller for linear time-varying (LTV) systems. To guarantee safety despite closed-loop data correlations, we derive a uniform-in-time, finite-sample confidence bound on the empirical predictor using vector-valued martingale concentration inequalities. Embedding this statistical uncertainty radius into a dynamically tightened constraint set rigorously ensures robust recursive feasibility and Input-to-State practical Stability (ISpS) with high probability. Simulations on LTI and LTV benchmarks demonstrate real-time tractability and strict constraint satisfaction.