Multiple Model Predictive Control for Nonlinear Systems Based on Self-Balanced Multimodel Decomposition

A gap-based measurement of nonlinearity (GMoN) is proposed to set up a criterion for multimodel decomposition (MMD) of nonlinear systems. Then, a self-balanced multimodel decomposition (SBMMD) approach based on GMoN is put forward for both single-inputsingle-output (SISO) and multiple-input-multiple-output (MIMO) nonlinear systems. Providing an initial value of the threshold and a step-length, a nonlinear system can be automatically partitioned into balanced subsystems: All the subregions have similar GMoNs that are approximated to the final threshold value. Based on the balanced model bank, a balanced multimodel model predictive controller (BMMPC) is designed. SISO and MIMO nonlinear systems have been analyzed and synthesized by the proposed SBMMD and BMMPC. It is confirmed that the SBMMD results in a more balanced model bank than other methods. Closed-loop simulations illustrate that the BMMPC has improved closed-loop performance compared to multimodel model predictive controllers (MMPCs) based on less unbalanced model banks. The balanced decomposition helps the BMMPC to achieve consistently good performance in the whole wide operating space.