Gap Metric based Offline Multiple Model Predictive Control

Multiple Model Predictive Control (MMPC) method is an efficient strategy to deal with the strongly nonlinear system with a large operating range. But sub-model selection and time-consuming online calculation are two practical problems for MMPC method. This paper develops an offline multiple model predictive control method to solve such problem. First, we utilize the gap metric to measure the difference between two linear models and present a neighborhood estimation algorithm. Then a class of linear models is established to approximate the nonlinear system. Based on the robust constrained MPC algorithm, we design a local off-line model predictive controller for each sub-model. In the offline part, a sequence of discrete states is chosen and the corresponding feedback gains are obtained. In the online part, the control law is easily acquired by selecting the gain according to the current state. This offline approach can reduce the online computation burden and be suitable for the fast time-varying process. After that, a switching rule between each sub-model is proposed to guarantee the global stability. Finally, the presented procedure is illustrated with the simulation example of a continuous stirred-tank reactor (CSTR).