Data-Efficient Control of Polynomial Systems via Physics-Guided Quadratic Constraints
For control engineers dealing with safety-critical systems where models are uncertain and data is limited, this work offers a less conservative and more data-efficient method for robust safety controller synthesis.
This work develops a physics-guided data-driven framework for synthesizing robust safety controllers for discrete-time nonlinear polynomial systems with unknown disturbances, using robust control barrier certificates to avoid unsafe regions. The approach reduces data requirements by integrating physical information as quadratic constraints, enabling robust safety analysis with significantly shorter trajectories compared to purely data-driven methods.
This work addresses the critical challenge of guaranteeing safety for complex dynamical systems where precise mathematical models are uncertain and data measurements are corrupted by noise. We develop a physics-guided, direct data-driven framework for synthesizing robust safety controllers for discrete-time nonlinear polynomial systems that are subject to unknown-but-bounded disturbances. To do so, we introduce a notion of safety through robust control barrier certificates, which ensure avoidance of unsafe regions, offering a less conservative alternative to existing methods based on robust invariant sets. To achieve data efficiency, we further integrate physical information, formulated as quadratic constraints on system and control matrices, with observed noisy data. This integration drastically reduces data requirements, enabling robust safety analysis with significantly shorter trajectories compared to purely data-driven methods. The proposed synthesis procedure is formulated as a sum-of-squares optimization program that systematically designs the barrier and its associated controller by leveraging both collected data and underlying physical laws. The efficacy of our framework is demonstrated on three benchmark systems, confirming its ability to offer robust safety guarantees with reduced data demands.