Towards non-linearly activated ZNN model for constrained manipulator trajectory tracking

Abstract

As a powerful method for time-varying problems solving, the zeroing neural network (ZNN) is widely applied in many practical applications that can be modeled as time-varying linear matrix equations (TVLME). Generally, existing ZNN models solve these TVLME problems in the ideal no noise situation without inequality constraints, but the TVLME with noises and inequality constraints are rarely considered. Therefore, a non-linear activation function is designed, and based on the non-linear activation function, a non-linearly activated ZNN (NAZNN) model is proposed for solving constrained TVLME (CTVLME) problems. The convergence and robustness of the proposed NAZNN model are verified theoretically, and simulation results further demonstrate the effectiveness and superiority of the NAZNN model in dealing with CTVLME and the constrained robot manipulator trajectory tracking problems. In addition, the wheeled robot trajectory tracking fault problems with physical constraints are also analyzed theoretically, and the proposed NAZNN model is also applied to the manipulator trajectory tracking fault problem, and the experimental results prove that the NAZNN model also deal with the manipulator trajectory tracking fault problem effectively.

Applications of Zeroing Neural Networks: A Survey

“…In 2022, Luo et al proposed a new hyperbolic tangent varying-parameter ZNNs (HTVP-ZNNs) with timevarying DCPs (designed convergence parameters) and a robust HTVP-ZNNs (HTVPR-ZNNs) [63], which exhibited excellent performance in trajectory tracking tasks of the robot. In 2023, Lan et al devised a non-linear activation function and leveraged it to propose a non-linearly activated ZNN (NAZNN) model [64]. The application of this NAZNN model in addressing the trajectory tracking fault problem of a manipulator effectively yielded positive results, as demonstrated through experimental analysis.…”

An Accelerated Dual-Integral Structure Zeroing Neural Network Resistant to Linear Noise for Dynamic Complex Matrix Inversion

“…It has been mentioned in many papers [23][24][25][26][27][28][29][30][31] that adding an activation function to some ZNN-like models can accelerate the convergence of the error function and enhance the model's ability to restrict noise. Therefore, we modified the ZNN model by adjusting its design formula to Ė(t) = −αΦ(E(t)) (9) in which, Φ(•): C n×n → C n×n is an activation function.…”

“…Leveraging its inherent dual-integral structure, the DISZNN model demonstrates superior performance in restricting linear noise for DCMI problems, as evidenced by theoretical analysis based on Laplace transforms. Moreover, numerous studies suggest that integrating activation functions (AFs) into ZNN models enhances noise tolerance and convergence performance [23][24][25][26][27][28][29][30][31]. Therefore, this paper proposes an accelerated dual-integral structure zeroing neural network (ADISZNN) by combining AFs with the DISZNN model to enhance its noise restriction capabilities against linear noise and accelerate convergence.…”