Digital Twins: McKean-Pontryagin Control for Partially Observed Physical Twins
It addresses the challenge of optimal control under partial observations, which is central to digital twin applications, but the method is an incremental hybrid of existing techniques.
The paper combines ensemble Kalman filter with McKean-Pontryagin control to enable optimal control of partially observed systems, demonstrating real-time applicability on Lorenz-63, Lorenz-96, and inverted pendulum examples.
Optimal control for fully observed diffusion processes is well established and has led to numerous numerical implementations based on, for example, Bellman's principle, model free reinforcement learning, Pontryagin's maximum principle, and model predictive control. In contrast, much fewer algorithms are available for optimal control of partially observed processes. However, this scenario is central to the digital twin paradigm, where a physical twin is partially observed and control laws are derived based on a digital twin. In this paper, we contribute to this challenge by combining data assimilation in the form of the ensemble Kalman filter with the recently proposed McKean-Pontryagin approach to stochastic optimal control. We derive forward evolving mean-field evolution equations for states and co-states which simultaneously allow for an online assimilation of data as well as an online computation of control laws. The proposed methodology is therefore perfectly suited for real time applications of digital twins. We present numerical results for controlled Lorenz-63 and Lorenz-96 systems as well as an inverted pendulum.