Physics-Informed Data-Driven Safe and Optimal Control Design

This paper introduces a physics-informed data-driven control design approach for discrete-time linear time-invariant systems. The control design will start from a robust control design when no data samples are available using physics information and progressively move towards a fully adaptive controller as more data becomes available. This will enhance the feasibility of designing a safe control system and elevate the performance of an optimal control system. It achieves this by integrating safety and performance specifications for systems that lie at the intersection of two information sets: the physics-informed set of possible system models and the data-conformity set of models. The side information for forming a physics-informed set is assumed to be provided based on the designer's knowledge of the bounds of the system parameters. This intersection set is non-empty if the prior knowledge includes the actual system model. Besides, it is smaller than physics-informed and data-conformity sets. Linear Matrix inequality conditions are provided to robustly satisfy the safety and performance of the systems that fall at the intersection set. Two applications are presented to verify the theoretical results: the safe hovering of a quadcopter and the quadratic regualtion of a Lithium-ion battery.