Data-Driven Subspace Predictive Control for a MIMO System

Subspace-based Model Predictive Control (SMPC) is a combination of a result in subspace system identification with Model Predictive Control (MPC) method. Particularly, it uses the subspace linear predictor equation to predict the future value of the system in the MPC implementation, instead of the usual state-space representation. The recursive subspace identification which updates the estimation of the extended observability matrix online is presented here for a Multi Input-Multi Output (MIMO) system specifically for a nonlinear Biological Waste Water Treatment Process. Givens rotation is applied for recursive updating of QR decomposition of a matrix in this SMPC. In SMPC, the need to have an explicit state-space representation of the system is abolished, resulting in a control algorithm that performs system identification and controller design in a single simultaneous step. Additionally, SMPC algorithm will inherit the numerical robustness typical of subspace-based methods thus giving us an easily deployable control implementation in adaptive framework.