Big data-driven predictive control for nonlinear systems—A trajectory cluster-based contraction approach

This article presents a novel contraction-based big data-driven predictive control (CBDPC) approach for nonlinear systems using the behavioural systems framework. The nonlinear behavioural space is partitioned into linear sub-behavioural spaces, represented by connected trajectory clusters. The controller drives the process to travel through multiple linear sub-behavioural spaces to reach the setpoint. By introducing the concepts of data-based contraction and differential dissipativity, a trajectory cluster-based control contraction metric and contraction condition are developed to guarantee incremental exponential stability of the controlled nonlinear system behaviour and attenuate the effect of linear sub-behaviour approximation errors on controlled output. Connected trajectory clusters are obtained via multi-view fuzzy clustering, which partitions nonlinear system behaviour (i.e., a set of input–output data trajectories) into connected linear sub-behaviours (i.e., trajectory subsets with intersections). Based on the above contraction and dissipativity conditions, an online data-driven predictive control approach using Hankel matrices is developed. The proposed approach is illustrated using a case study on control of an aluminium smelting process, which demonstrates the control performance achieved by the CBDPC approach.