Non-PDC Interval Type-2 Fuzzy Model Predictive Microclimate Control of a Greenhouse

Abstract

Greenhouse climate control is known as a challenging task since it is characterized by the strong interaction among the involved variables, the time-varying uncertainties, and the external disturbances that severely affect its internal environment. In this paper, a discrete-time fuzzy model predictive control approach of a greenhouse is investigated. An interval type-2 (IT2) Takagi–Sugeno fuzzy model is employed to represent the nonlinear dynamics of the plant subject to parameter uncertainties, which are effectively captured by interval membership functions. To design the fuzzy model predictive controller, an optimization problem which minimizes a quadratic cost function respecting the input and state constraints is formulated and solved at each sampling instant in the prediction time horizon. By introducing a non-parallel distributed compensation (non-PDC) design concept and based on the non-quadratic Lyapunov function, less conservative conditions are developed in terms of linear matrix inequality to guarantee the stability analysis. Simulation results illustrate the effectiveness of the proposed control approach in leading to promote a comfortable greenhouse microclimate for the growth of the crops.