A nonconvex function activated noise-tolerant neurodynamic model aided with Fischer-Burmeister function for time-varying quadratic programming in the presence of noises

Abstract

Time-varying quadratic programming problems (TVQPPs) with equality and inequality constraints often arise in the fields of scientific computation and engineering application. Zeroing neural network (ZNN), being a special kind of recurrent neural network, has shown powerful capabilities to compute a variety of zeroing finding problems with monotonically increasing odd activation function. However, the projection sets of nonconvex activation function are obviously excluded, which means a general conclusion remain unexplored. In addition, noises are always ubiquitous in actual applications. Nevertheless, most existing ZNN-based models usually assume that the solving process is free of noise before the calculation. In this paper, a general zeroing neural network model with nonconvex activated function (GZNNM-NAF) and a general noise-tolerant zeroing neural network model with nonconvex activated function (GNTZNNM-NAF), which are also viewed as ZNN-type models, are developed by the inspiration of the traditional ZNN model from a control-based perspective. The ZNN-type models break the limitation of the traditional ZNN models of activation function, which allows nonconvex sets for projection operations and combines nonlinear complementary function for dealing with inequality constraints arising in TVQPPs. Moreover, theoretical results indicate that the ZNN-type models globally converge to time-varying optimal solution of TVQPPs with equality and inequality constraints under the noise circumstance. According to the different cases of nonconvex activation function, robustness analyses are demonstrated in detail for TVQPPs. It may enlarge the scope of the proposed method, especially in the field of practical application. Finally, a numerical example and an application example to manipulator motion generation are analyzed to verify the superiority and robustness of the developed ZNN-type models for TVQPPs with different measurement noises.