# Leibniz MMS Days 2023 - Abstract

**Sommer, David**

*Robust model predictive control for digital twins using feedback laws*

Real-time model updates and model-based controllers are essential parts of digital twins of dynamical systems. Due to modeling errors, the state of the physical twin can not be expected to match the predictions of the digital twin exactly, however. Controls that consider the current, unpredictable state of the physical twin, known as "closed-loop" or "feedback" controls, differ from öpen-loop" controls, which rely solely on the state during planning. Depending on the rate of change in the physical counterpart, a digital twin operating on open-loop controls may need to compute new controls within seconds or even milliseconds. This technique is known as Model Predictive control (MPC). In this talk, we explore possibilities and challenges of MPC with true feedback laws. Examples range from the simple linear quadratic case, encountered in the air conditioning problem, to more sophisticated problems which require solutions of the Hamilton Jacobi Bellman partial differential equation.