TraCPro-BDPC: Trajectory Cluster-Based Probabilistic Big Data-Driven Predictive Control for Nonlinear Processes

A trajectory cluster-based probabilistic big data-driven predictive control (TraCPro-BDPC) approach is proposed for nonlinear processes in the behavioral systems framework. With a big dataset of input-output data trajectories, the nonlinear process behavior is partitioned into multiple linear sub-behaviors (characterized by the trajectory clusters) offline via clustering. To control the nonlinear process outside these linear sub-behaviors, a probabilistic system behavior interpolation method is proposed for online control based on the known trajectory clusters. In each receding horizon, the interpolation method quantifies the stochastic uncertainty of the online interpolated linear sub-behavior by interpolating a probability density function of the data trajectory. Based on polynomial chaos expansions, an online big data-driven predictive control approach is developed to deal with the stochastic uncertainty propagation of online linear sub-behavior interpolation. The proposed approach is illustrated by an example of the control of an aluminum smelting process.