Design and implementation of a sub-optimal explicit mpc using a novel complexity reduction approach based on fuzzy reshaped active regions

The Explicit Model Predictive Control (EMPC) has emerged as a powerful technique to solve the optimization problem for embedded applications. Despite practical obstacles in the implementation of EMPC, the main drawback of Model Predictive Control (MPC), due to its need for repetitively solving optimization problems, is removed. This paper addresses the complexity of online computation and the required memory for storing the data in EMPC implementation. In this paper, a novel reshaping method is applied for active region selection in order to have regular boundaries in polyhedron definitions. In this approach, several improvements have been achieved. First, it employs low memory for practical implementation compared to the traditional EMPC. Next, because of less number of new polyhedrons, searching time among explicit look-up table is decreased, so the overall implementation speed is increased. For this purpose, using fuzzy clustering, a reshaping method for traditional polyhedrons is introduced as Fuzzy Explicit Model Predictive Control, then a novel fuzzy-based Piece-Wise Affine explicit formulation is developed for control action calculation. Stability of the proposed scheme is investigated using the Lyapunov stability criterion. The proposed algorithm is tested on a nonlinear chemical reactor of propylene glycol as an industrial pilot plant. The simulation tests show that the proposed approach can significantly outperform the traditional explicit MPC methods in real-time implementation.