Model predictive control of nonlinear hybrid systems with discrete inputs employing a hybrid fuzzy model

Abstract

The paper deals with model predictive control (MPC) of nonlinear hybrid systems with discrete inputs based on reachability analysis. In order to implement a MPC algorithm, a model of the process that we are dealing with is needed. In the paper, a hybrid fuzzy modelling approach is proposed. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for hybrid fuzzy modelling purposes is tackled. An efficient method of identification of the hybrid fuzzy model is also discussed. An algorithm that is–due to its MPC nature–suitable for controlling a wide spectrum of systems (provided that they have discrete inputs only) is presented. The benefits of the algorithm employing a hybrid fuzzy model are verified on a batch reactor example. The results suggest that by suitably determining the cost function, satisfactory control can be attained, even when dealing with complex hybrid–nonlinear–stiff systems such as the batch reactor. Finally, a comparison between MPC employing a hybrid linear model and a hybrid fuzzy model is carried out. It has been established that the latter approach clearly outperforms the approach where a linear model is used.