Dynamic nonlinear equations (DNEs) are essential for modeling complex systems in various fields due to their ability to capture real-world phenomena. However, the solution of DNEs presents significant challenges, especially in industrial settings where periodic noise often compromises solution fidelity. To tackle this challenge, we propose a novel approach called Periodic Noise Suppression Neural Dynamic (PNSND), which leverages the gradient descent approach and incorporates velocity compensation to overcome the limitations of the traditional Gradient Neural Dynamic (GND) model. Additionally, the PNSND model aims to suppress periodic noise by addressing its harmonic properties according to the method of Fourier decomposition of harmonics. In the paper, we explore the performance of convergence and robustness of the PNSND model. Moreover, we demonstrate the effectiveness of the PNSND model in addressing dynamic nonlinear problems under periodic noise interference through its application to robotic arm, highlighting its practical significance in industrial contexts.

Solving time-varying algebraic Riccati equations (TVAREs) is crucial in sound source tracking and optimal control. It is worth noting that previous studies have focused primarily on solving static algebraic Riccati equations (AREs) or interference-free TVAREs. Nonetheless, in real-world solution systems, AREs are often time-varying and subject to a variety of external disturbances. To address these problems, we propose two strong initial state discrete noise-resistant zeroing neurodynamics (SDRZND) algorithms for determining the solutions to TVAREs. First, we introduce a bounded smoothing of the strong initial state coefficient to accelerate algorithm convergence while avoiding the additional impulse noise that non-smoothed coefficients in the discrete algorithm might generate. Then, an integral feedback term is designed and integrated with this coefficient to enhance the algorithm’s robustness. Subsequently, to further improve the algorithm’s flexibility, we introduce a variable time step, leading to the SDRZND-Euler (SDRZND-E) and SDRZND-Taylor-Zhang (SDRZND-TZ) algorithms presented in this paper. Lastly, the effectiveness, noise resistance, and practicality of these algorithms are verified through theoretical analysis, numerical simulations, and sound source tracking experiments.

Nonlinear optimization with equation constraints has wide applications in intelligent control systems, acoustic signal processing, etc. Thus, effectively tackling the nonlinear optimization problems with equation constraints is of great significance for the advancement of these fields. Current discrete-time neurodynamics predominantly addresses unperturbed optimization scenarios, exhibiting inherent sensitivity to external noise, which limits the practical application of these methods. To address this issue, we propose a discrete-time noise-suppressed neurodynamics (DTNSN) model in this paper. First, the model integrates the static optimization stability of the gradient-based neurodynamics (GND) model with the time-varying tracking capability of the zeroing neurodynamics (ZND) model. Then, an integral feedback term is introduced to suppress external noise disturbances, thereby enhancing the robustness of the model. Additionally, to facilitate implementation on digital hardware, we employ an explicit linear three-step discretization method to obtain the proposed DTNSN model. Finally, the convergence performance, noise suppression capability, and practicality of the model are validated through theoretical analysis, numerical simulations, and acoustic source localization experiments. The model is applicable to the fields of intelligent control systems, acoustic signal processing, and industrial automation, providing new tools for real-time optimization in noisy environments.