Data-driven non-Gaussian stochastic dynamical system identification meets knowledge-based model predictive control

Randomness and nonlinearity are essential properties of the real world, and their interaction gives rise to highly complex phenomena. With the advancement of technology, merely observing data of the current system state is no longer sufficient for prediction and application in various fields. Consequently, extracting the nonlinear evolution nature of the system from noisy data has become a prominent and challenging issue. To address this, we propose an integrated approach that combines data-driven stochastic model identification with a knowledge-based model predictive control strategy. By leveraging high-precision model identification, our data-driven control design is particularly effective for continuous target tracking problems that are difficult to address using traditional precise-model-based control theory. Furthermore, the central challenge in data science lies in maximizing the informational value of datasets while minimizing the effects of observation noise. In this study, we propose and rigorously demonstrate the stochastic Occam’s razor principle, a stochastic error estimation theory that evaluates and enhances the design of data-driven schemes to mitigate the effect of observation noise. Notably, our approach offers valuable insights for contemporary data-driven, end-to-end control challenges, particularly those involving uncertain governing equations and substantial non-Gaussian observation noise.