Model-based Predictive Control for Spatially-distributed Systems Using Dimensional Reduction Models

In this paper, a low-dimensional multiple-input and multiple-output (MIMO) model predictive control (MPC) configuration is presented for partial differential equation (PDE) unknown spatially-distributed systems (SDSs). First, the dimension reduction with principal component analysis (PCA) is used to transform the high-dimensional spatio-temporal data into a low-dimensional time domain. The MPC strategy is proposed based on the online correction low-dimensional models, where the state of the system at a previous time is used to correct the output of low-dimensional models. Sufficient conditions for closed-loop stability are presented and proven. Simulations demonstrate the accuracy and efficiency of the proposed methodologies.