Physics-informed data-driven control without persistence of excitation

2025-04-11

AI Summary

System re-identification becomes challenging under insufficient excitation data—i.e., when persistent excitation conditions are not satisfied. Method: This paper proposes a physics-informed, data-driven control framework that integrates physical prior knowledge—specifically, boundedness of system matrix norms—to construct an interpolation-based data generalization mechanism. It combines physics embedding with robust system identification to jointly ensure safety constraint satisfaction, energy-optimal policy synthesis, and high-accuracy prediction of unmodeled dynamics—even with limited data. Contribution/Results: The approach significantly improves control reliability and generalization in low-data regimes. Experiments demonstrate that physical priors effectively compensate for data scarcity, enabling safe, optimal, and robust control under stringent data limitations. This work establishes a novel paradigm for safety-critical control in data-constrained settings.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

We show that data that is not sufficiently informative to allow for system re-identification can still provide meaningful information when combined with external or physical knowledge of the system, such as bounded system matrix norms. We then illustrate how this information can be leveraged for safety and energy minimization problems and to enhance predictions in unmodelled dynamics. This preliminary work outlines key ideas toward using limited data for effective control by integrating physical knowledge of the system and exploiting interpolation conditions.

Problem

• Leveraging limited data with physical knowledge for control
• Enhancing predictions in unmodelled dynamics using data
• Combining system norms and data for safety optimization

Innovation

• Combining limited data with physical knowledge
• Leveraging system norms for safety optimization
• Enhancing predictions via interpolation conditions