A RBF Neural Network System for Solving Fuzzy Optimal Control Problems Depending on Generalized Hukuhara Derivatives

In this paper, an intelligence approach based on radial basis function neural networks (RBFNNs) is used for solving fuzzy optimal control problems, utilizing the generalized Hukuhara derivatives. At the first step, we consider the fuzzy Euler-Lagrange conditions for both fuzzy unconstrained and constrained variational problems and Pontryagin maximum principle (PMP) for fuzzy optimal control problems, both of them depending on the generalized Hukuhara derivatives. The necessary optimality conditions for these problems are examined in the form of two-point boundary value problems (TPBVPs). A fuzzy neural network approach that utilizes of radial basis functions (RBFs) as its activation functions for one of the hidden layers is described to approximate the solution of the related TPBVP. This neural network uses the center points of RBFs as the training dataset, and the Levenberg-Marquardt algorithm is selected as the optimizer. By relying on the ability of RBFNN as function approximator, the fuzzy solutions of variables (state, co-state and control) are substituted in the associated TPBVP. The obtained algebraic nonlinear equations system is then converted into an error function minimization problem. A learning scheme based on the Levenberg-Marquardt algorithm is employed as the optimizer to derive the adjustable parameters of fuzzy solutions. In order to clarify the effectiveness of the studied RBFNN, some numerical results are supplied.