Abstract— A fuzzy optimal control model was formulated minimizing the objective function with discounted cost for the length of infinite horizon. We developed an equation of optimality in case of fuzzy optimal control problem. We revisited a special fuzzy control model with quadratic objective functional form for linear Liu’s fuzzy control system. As an application, we investigated the infinite horizon production inventory planning problem with nonzero discount rate. We employed fuzzy optimal control to model inventory production planning problem with fuzzy variables and solved.