Big data-driven predictive control for nonlinear systems based on kernel density estimation of data trajectories

A big data-driven predictive control approach for nonlinear systems is proposed based on the kernel density estimation of data trajectories (KDE-BDPC) in the behavioural systems framework, which aims to control the nonlinear process in the regions where only limited data are available. The nonlinear process behaviour (a set of input–output variable trajectories) can be partitioned into linear sub-behaviours (trajectory clusters) offline via multi-view clustering of collected data trajectories. To operate the nonlinear process behaviour outside the existing linear sub-behaviours, we propose a data-driven system behaviour approximation approach that can interpolate linear sub-behaviours based on the density estimation of existing data trajectories and linear subspace distance. Based on online interpolated linear sub-behaviours, an online big data-driven predictive controller is designed, which includes a path search to minimise uncertainty. The proposed approach is illustrated by a vanadium flow battery control problem.