Abstract
The time-varying complex-valued Sylvester equation (TVCVSE) often appears in many fields such as control and communication engineering. Classical recurrent neural network (RNN) models (e.g., gradient neural network (GNN) and zeroing neural network (ZNN)) are often used to solve such problems. This paper proposes an adaptive coefficient and non-convex projection zeroing neural network (ACNPZNN) model for solving TVCVSE. To enhance its adaptability as residual error decreasing as time, an adaptive coefficient is designed based on residual error. Meanwhile, this paper breaks the convex constraint by constructing two complex-valued non-convex projection activation functions from two different aspects. Moreover, the global convergence of the proposed model is proved, the anti-noise performance of the ACNPZNN model under different noises is theoretically analyzed. Finally, simulation experiments are provided to compare the convergence performance of different models, which simultaneously verifies the effectiveness and superiority of the proposed model.
Highlights
I N recent years, Sylvester equation has become widely available for many research fields, such as control engineering, image processing, and communication engineering [1]–[6], etc
On the basis of the above research, this paper extends the application range of solving time-varying Sylvester equation (TVSE) from the real-valued domain to the complex-valued domain and proposes a complexvalued Zeroing neural network (ZNN) [32] model to solve time-varying complexvalued Sylvester equation (TVCVSE)
A novel adaptive complex-valued zeroing neural network (ACNPZNN) model is creatively proposed to solve the time-varying complex-valued Sylvester equation (TVCVSE) in this paper, which can efficiently deal with complex-valued time-varying problem and ensure the high precision of the solution results
Summary
I N recent years, Sylvester equation has become widely available for many research fields, such as control engineering, image processing, and communication engineering [1]–[6], etc. This paper proposes adaptive coefficients [33] to construct a adaptive coefficient and non-convex projection zeroing neural network (ACNPZNN) model, which can overcome the excessively long convergence time and convergence accuracy of the ZNN model, and achieve the effect of adaptive system changes. A novel adaptive complex-valued zeroing neural network (ACNPZNN) model is creatively proposed to solve the TVCVSE in this paper, which can efficiently deal with complex-valued time-varying problem and ensure the high precision of the solution results. A series of experiments show that the simulation results basically coincide with the theoretical analyses, which verify the superiority and feasibility of the proposed ACNPZNN model
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