A Stable and Admissible Explicit Solution to Fuzzy Predictive Control using polyhedral invariant sets

One of the main problems in Model Predictive control MPC is the lack of guaranteed feasibility and stability. In this paper we propose a strategy to resolve the optimization problem associated with fuzzy predictive control to find a solution that is both stable and admissible. The proposed explicit approach, combined with the theory of invariant sets, provides a secure and admissible solution for the optimization problem. The approach begins by applying the principles of decision making in a fuzzy environment, specifically the Bellman Zadeh approach. Next, we divide the state space into separate regions the objective of this separation is to identify the state region that contains the appropriate solutions. We start with the terminal region and then working down, developing a set of permissible control laws for each region. The simulation results confirm that our strategy effectively addresses the problems of feasibility and stability in Model Predictive Control.