Modified Noise-Immune Fuzzy Neural Network for Solving the Quadratic Programming With Equality Constraint Problem.

Quadratic programming with equality constraint (QPEC) problems have extensive applicability in many industries as a versatile nonlinear programming modeling tool. However, noise interference is inevitable when solving QPEC problems in complex environments, so research on noise interference suppression or elimination methods is of great interest. This article proposes a modified noise-immune fuzzy neural network (MNIFNN) model and use it to solve QPEC problems. Compared with the traditional gradient recurrent neural network (TGRNN) and traditional zeroing recurrent neural network (TZRNN) models, the MNIFNN model has the advantage of inherent noise tolerance ability and stronger robustness, which is achieved by combining proportional, integral, and differential elements. Furthermore, the design parameters of the MNIFNN model adopt two disparate fuzzy parameters generated by two fuzzy logic systems (FLSs) related to the residual and residual integral term, which can improve the adaptability of the MNIFNN model. Numerical simulations demonstrate the effectiveness of the MNIFNN model in noise tolerance.

A Fixed-Time Noise-Tolerance ZNN Model for Time-Variant Inequality-Constrained Quaternion Matrix Least-Squares Problem.

Presently, numerical algorithms for solving quaternion least-squares problems have been intensively studied and utilized in various disciplines. However, they are unsuitable for solving the corresponding time-variant problems, and thus few studies have explored the solution to the time-variant inequality-constrained quaternion matrix least-squares problem (TVIQLS). To do so, this article designs a fixed-time noise-tolerance zeroing neural network (FTNTZNN) model to determine the solution of the TVIQLS in a complex environment by exploiting the integral structure and the improved activation function (AF). The FTNTZNN model is immune to the effects of initial values and external noise, which is much superior to the conventional zeroing neural network (CZNN) models. Besides, detailed theoretical derivations about the global stability, the fixed-time (FXT) convergence, and the robustness of the FTNTZNN model are provided. Simulation results indicate that the FTNTZNN model has a shorter convergence time and superior robustness compared to other zeroing neural network (ZNN) models activated by ordinary AFs. At last, the construction method of the FTNTZNN model is successfully applied to the synchronization of Lorenz chaotic systems (LCSs), which shows the practical application value of the FTNTZNN model.