Optimal Control Methods for Fuzzy Optimal Control Problem

We have made several adjustmentsto fulfill the necessary requirements for optimal control problems based on fuzzy concepts for the LQR method by implementing the horizontal membership function (HMF) concept and also utilizing the definition of differentiation with a granular approach. We then construct an illustrative example of fuzzy optimal control problems for PMP and LQR methods by determining fuzzy control in the description of a Gaussian membership function. The fuzzy control, which is declared as a membership function, is expected to facilitate the optimal control process applied to the fuzzification process of a fuzzy model, such as the Takagi-Sugeno (or Takagi-Sugeno-Kang) fuzzy model.Fuzzy models of the Takagi-Sugeno (or Takagi-Sugeno-Kang) type aim to represent systems or plants that are non-linear. Therefore, we have PMP for optimal control problems with a fuzzy approach and LQR for optimal control problems with a fuzzy approach. Both optimal control methods involve many variational calculus (variational problems) that require an approach relevant with the idea of Euler-Lagrange. Hereafter, we find a solution to the fuzzy optimal control problems for PMP and LQR analytically. We obtain optimal fuzzy state and optimal fuzzy control. Finally, we apply Simulink (Matlab) to show graphics of the optimal fuzzy state and optimal fuzzy control.