Different Zhang functions resulting in different ZNN models demonstrated via time-varying linear matrix–vector inequalities solving

Abstract

Our previous work shows that Zhang neural network (ZNN) has the higher efficiency and better performance for solving online time-varying linear matrix–vector inequalities, as compared to the conventional gradient neural network. In this paper, introducing the concept of Zhang function, we further investigate the problem of time-varying linear matrix–vector inequalities solving. Specifically, by defining three different Zhang functions, three types of ZNN models are further elaborately constructed to solve time-varying linear matrix–vector inequalities. The first ZNN model is based on a vector-valued lower-bounded Zhang function and is termed ZNN-1 model. The second one is based on a vector-valued lower-unbounded Zhang function and is termed ZNN-2 model. The third one is based on a transformed lower-unbounded Zhang function and is termed ZNN-3 model. Compared with the ZNN-1 model for solving time-varying linear matrix–vector inequalities, it is surprisedly discovered that the ZNN-2 model incorporates the ZNN-1 model as its special case. Besides, we put research emphasis on the ZNN-3 model for solving time-varying linear matrix–vector inequalities (including its design process, theoretical analysis and simulation verification). When power-sum activation functions are exploited, the ZNN-3 model possesses the property of superior convergence and better accuracy. Computer-simulation results further verify and demonstrate the theoretical analysis and efficacy of the ZNN-3 model for solving time-varying linear matrix–vector inequalities.