As an effective tool for solving dynamic complex value problems, especially dynamic complex value matrix inversion (DCVMI), the complex value zeroing neural network (CVZNN) has been widely applied in various practical industrial fields. However, previous complex value zeroing neural network (PCVZNN) models only achieve unsatisfactory exponential or finite time convergence, which usually does not conform to actual practical situation. Different from PCVZNN models, a complex-valued variant parameter robust ZNN model (CVVPRZNN) with both fixed-time convergence and robustness for solving DCVMI is proposed in this paper. The fixed-time convergence and noise suppression ability of the CVVPRZNN model for solving DCVMI are strictly deduced. Then, three comparative numerical experiments for DCVMI solving, dynamic circuit currents computing and manipulator trajectory tracking of the proposed CVVPRZNN model with other existing PCVZNN models are provided for demonstrating its better solution performances and higher practical application value. It should be noted that the experimental results indicate that regardless of whether it is disturbed by noise or not, the CVVPRZNN model only requires about 0.01 s to complete the corresponding solving task. However, in the same experimental environment, other models either cannot complete the solving task at all, or require about 8 s which is almost 800 times the solving time of the CVVPRZNN model to complete the corresponding dynamic problem solving.

Cryptography is the core of information security. Among various types of ciphers, the traditional Hill Cipher (THC) is a static alternative cipher based on the basic matrix theory. Stuck in the security and real-time issues of the THC with time-invariant key, this paper studies a dynamic novel Hill Cipher (NHC) with time-variant key for the first time. To ensure the fast decryption of the NHC, this work chooses the zeroing neural network (ZNN) which plays vital important role in solving dynamic problems as the decryption algorithm of NHC to solve the time-variant key inversion (TVKI) matrix. Specifically, a new robust fixed-time convergent activation function (NRFT-AF) and a new time-variant convergence factor (NTv-CF) are designed, and thus a new-type zeroing neural network model (NT-ZNN) is constructed by them for solving the TVKI. By virtue of abundant rigorous mathematical derivation, the fixed-time convergence and robustness of NT-ZNN model for solving the TVKI under the cases without noise and with noise are theoretically demonstrated in detail. Moreover, the NHC is also applied to the encryption and decryption experiments of different strings and RGB color image to validate its reliability. Then, comparative simulation results of the NT-ZNN model with conventional-type zeroing neural network (CT-ZNN) models constructed by other existing activation functions (AFs) and convergence factors (CFs) for solving the TVKI are given, and the superiority of the NT-ZNN model in NHC decryption is further verified.

The zeroing neural network (ZNN) model, a powerful approach for addressing time-varying problems, has been extensively applied in the calculation and optimization fields. In this article, a new pattern activation function, the power piecewise activation function (PPAF), is proposed to establish a predefined fixed-time convergent ZNN (PFTZNN) for finding solutions to the time-varying quadratic programming problem. In comparison with the traditional activation functions, multisegmentation is a remarkable feature of the PPAF; consequently, the advantage of PPAF is that its parameters can be flexibly adjusted according to actual needs. Specifically, because of the multisegment characteristics of the PPAF, the convergence speed of the PPAF-activated PFTZNN model can be flexibly adjusted based on distinct requirements. The fixed-time convergence property of the PPAF-activated PFTZNN model is validated by detailed mathematical theoretical analysis, and its upper bound convergence time is directly calculated. Then, the comparative simulation results of the PPAF-activated PFTZNN model with other existing ZNN models for time-varying quadratic programming are provided for the further verification of its superior convergence speed and robustness. In addition, the proposed PFTZNN model is applied for dual-arm manipulator cooperative trajectory tracking, and its practical application ability is demonstrated by united simulation experiments of MATLAB and Robot studio. Finally, the PFTZNN model is also applied to control a real dual-arm manipulator to complete the trajectory tracking task, which further validates its superior performance together and widespread applicability.

In this paper, the tracking performance limitation of networked control systems (NCSs) is studied. The NCSs are considered as continuous-time linear multi-input multioutput (MIMO) systems with random reference noises. The controlled plants include unstable poles and nonminimum phase (NMP) zeros. The output feedback path is affected by multiple communication constraints. We focus on some basic communication constraints, including additive white noise (AWN), quantization noise, bandwidth, as well as encoder-decoder. The system performance is evaluated with the tracking error energy, and used a two-degree-of-freedom (2DOF) controller. The explicit representation of the tracking performance is given in this paper. The results indicate the tracking performance limitations rely to internal characteristics of the plant (unstable poles and NMP zeros), reference noises [the reference noise power distribution (RNPD) and its directions], and the characteristics of communication constraints. The characteristics of communication constraints include communication noise power distribution (CNPD); quantization noise power distribution (QNPD), and their distribution directions; transform bandwidth allocation (TBA); transform encoder-decoder allocation (TEA), and their allocation directions; and NMP zeros and MP part of bandwidth. Moreover, the tracking performance limitations are also affected by the angles between the each transform NMP zero direction and RNPD direction, and these angles between each transform unstable poles direction and the direction of communication constraint distribution/allocation. In addition, for MIMO NCSs, bandwidth (there are not identical two channels) can always affect the direction of unstable poles, and the channel allocation of bandwidth and encode-decode may be used for a feasible method for the performance allocation of each channel. Finally, an instance is given for verifying the effectiveness of the theoretical outcomes.