A Predefined-Time Fuzzy Adaptive RNN for Time-Dependent Bound-Constrained Nonlinear Optimization With Applications

Recently, recurrent neural network (RNN) models have been extensively investigated for addressing time-dependent nonlinear optimization problems. However, few existing RNN models take account of bound constraints, noise resistance, and predefined-time convergence (PTC) simultaneously, which leads to many challenges in practical applications to a certain extent. Moreover, when solving time-dependent bound-constrained nonlinear optimization (TDBCNO) problems, most existing RNN models directly employ nonlinear complementary problem functions to convert bound constraints into inequality constraints. This approach inevitably introduces higher-dimensional coefficient matrices and a larger number of Lagrange multipliers, thereby increasing the overall computational complexity. To deal with these issues, a predefined-time fuzzy adaptive recurrent neural network (PTFA-RNN) model is proposed to efficiently tackle TDBCNO problems under various noises. By introducing the first-order optimality conditions, the dimensions of coefficient matrices and the number of Lagrange multipliers are effectively reduced. Furthermore, a novel activation function is constructed by integrating a fuzzy control system, enabling the PTFA-RNN model to achieve fast PTC and strong robustness. Theoretical analyses rigorously reveal the global stability, PTC, and strong robustness of the PTFA-RNN model. Numerical experiments validate the theoretical results and reveal that the PTFA-RNN model possesses shorter convergence time and better robustness. Finally, the applications to the dimension reduction on principal component analysis and manipulator control further illustrate the practicality and validity of the PTFA-RNN model.