Researchers' weighted norm method improves nonlinear system control
A new regularization trick localizes predictions without discarding any data.
Data-driven control methods like DeePC typically assume linearity, relying on Willems' fundamental lemma. For nonlinear systems, this assumption breaks down because dynamics vary across operating regions. The new framework introduces a weighted regularization that assigns higher importance to data points closer to the current operating point, effectively localizing the predictor without removing any data. This preserves the full data matrix and its rank, ensuring a well-posed optimization problem.
In numerical tests on a nonlinear two-tank system, the method matched or exceeded the performance of hard data-selection schemes. By avoiding data discarding, it maintains feasibility and robustness. The approach offers a practical path to applying predictive control to real-world nonlinear systems without the complexity of explicit model identification.
- Uses weighted norm regularization to prioritize data by proximity to current operating point.
- Preserves full data matrix and rank, ensuring well-posed optimization and feasibility.
- Outperforms hard data-selection schemes in numerical tests on a two-tank nonlinear system.
Why It Matters
Enables robust predictive control for real-world nonlinear systems without discarding valuable data.