Adaptive Behavioral Predictive Control: State-Free Regulation Without Hankel Weights

TL;DR

This paper introduces ABPC, a novel adaptive predictive control framework that operates in real-time without Hankel matrices, using kernel methods for enhanced model expressiveness and demonstrated effectiveness on nonlinear systems.

Contribution

It proposes a state-free, online adaptive control method leveraging kernel--recursive least squares, avoiding batch Hankel matrices, and extending model flexibility with nonlinear kernels.

Findings

Effective control on Hammerstein and NARX systems

Highlights importance of dictionary alignment and feature selection

Demonstrates computational feasibility and reproducibility

Abstract

This paper presents adaptive behavioral predictive control (ABPC), an indirect adaptive predictive control framework operating on streaming data. An LPV--ARX predictor is identified online via kernel--recursive least squares and used to compute closed-form predictive control sequences over a finite horizon, avoiding batch Hankel constructions and iterative optimization. Nonlinear kernel dictionaries extend model expressiveness within a behavioral formulation. Numerical studies on Hammerstein and NARX systems demonstrate effective performance when the dictionary aligns with the plant class and highlight conditioning and feature-selection effects. The paper emphasizes numerical simulation, computational feasibility, and reproducibility.