Descriptor-Form-Based Optimum Control Design Approach for the Polynomial Fuzzy Model with Input Constraints

This paper focuses on introducing an optimum control design methodology founded on descriptor form for the polynomial fuzzy model (PFM) with input constraints. The methodology commences by representing the closed-loop system of the PFM with the fuzzy controller based on parallel distributed compensation in a descriptor form. After that, a multiple Lyapunov function is applied to obtain more relaxed results for the stability analysis of the optimum control design. The optimum control design aims to minimize the upper bound of a given objective function. Besides considering practical situations, the study also integrates the input constraints into the optimum control design. The validity of the proposed design is substantiated through the provision of three simulation instances. Through the first two instances, it becomes apparent that the proposed design surpasses conventional optimum control design approaches for the PFM, yielding superior and more relaxed results. In the third instance, applying a bicycle dynamic model with an input constraint underscores the superior applicability of the proposed optimum control design approach in comparison to other existing methods.