On Feasibility and Asymptotically Stability of Switched Systems Using Adaptive Multi-Model Predictive Control

The present paper attempts to design an adaptive multi-model predictive control strategy for strongly nonlinear or switched systems with various operating points. The proposed control system guarantees the feasibility and the asymptotic stability of the closed-loop system, considering various challenges such as inherent uncertainties in the local models constituting the model bank, limited prediction/control horizons, and set point changes. To this end, four fundamental challenges in this area, namely guaranteeing feasibility throughout the region assigned to each subspace, ensuring asymptotic stability in each subspace considering the inherent uncertainties of the local models, guaranteeing feasibility and asymptotic stability during changes in the set point and switching between the subspaces, are addressed. By introducing transferring mode concept, this paper presents a novel method for guaranteeing the feasibility and stability of the switched systems without the need for increasing the prediction/control horizons or decreasing the size of the feasibility region. The proposed control structure uses a supervisor algorithm along with a soft-switching technique. The supervisor algorithm is responsible for determining the suitable local model/controller pair, determining the operational mode of the control system, managing the soft switching, and specifying the control objectives in accordance with the defined set point. The efficiency of the proposed control strategy is demonstrated by simulating a Continuous Stirred Tank Reactor (CSTR) as the controlled system. Based on the results, the proposed controller is able to guarantee the feasibility and stability of highly nonlinear and switched systems in a wide operating region under set point changes and uncertainties in the local models.