DDKPC Algorithm Guarantees Stability for Nonlinear Control Systems

This paper from arXiv (July 2026) by Wenjie Liu, Yifei Li, Gang Wang, and Lihua Xie presents a theoretical analysis of a data-driven kernel-based predictive control (DDKPC) scheme for nonlinear systems. The approach constructs a multi-step predictor using kernel methods and the representer theorem, implicitly capturing nonlinear dynamics from input-output data. For the nominal case with noise-free data, the authors prove that DDKPC guarantees recursive feasibility and closed-loop stability provided the prediction horizon is sufficiently long and the kernel representation error is small. To enable real-time implementation, they introduce a penalty relaxation formulation that reduces computational burden from nonconvex implicit constraints.

The framework is robustified against measurement noise by aggregating representation mismatch and bounded noise into a single uncertainty bound. It is further extended to slowly time-varying nonlinear systems by periodically updating the kernel predictor using a fixed-budget online dictionary managed by the approximate linear dependency (ALD) criterion. Under suitable conditions on the rate of variation and online prediction error, recursive feasibility and practical closed-loop stability are preserved. Numerical examples illustrate the effectiveness of the approach, making DDKPC a promising tool for safe, data-driven nonlinear control without requiring explicit system models.