New zeroing NN models with nonconvex saturated activation functions in noisy environments for quadratic minimization dynamics and control

• Published in: Journal of computational and applied mathematics 2024-10, Vol.448, p.115884, Article 115884
• Main Authors: Luo, Tangtao, Wang, Guancheng, Xiao, Xiuchun
• Format: Article
• Language: English
• Subjects: Dynamic quadratic minimization; Finite-time convergence; Nonconvex saturation activation function; Robustness; Zeroing neural network
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2024.115884

Fast and accurate solutions are of great importance to dynamic quadratic minimization (DQM) problems in many fields of engineering and science. By making a general survey of existing methods, DQM problems are capable of being solved very validly while there is still a lack of a superior performance method to face a noisy environment. To tolerate the ubiquitous noise, a zeroing neural network with a nonconvex saturated activation function model (ZNN-NCS) is proposed in this paper. The ZNN-NCS model exhibits high tolerance for bounded noise and responds to noise beyond the boundary, thereby monitoring environmental noise to a certain extent. Furthermore, combined with the control theory, an integral enhanced ZNN-NCS (IEZNN-NCS) model is proposed to adapt to the noise with unknown bounded. The IEZNN-NCS model has an effective ability to suppress noise that exceeds predefined boundary and noise that occurs suddenly. Afterwards, rigorous theoretical proofs of proposed models are conducted, and their global convergence and high robustness performance are demonstrated from a mathematical point of view. Finally, a special DQM problem is solved using the proposed models to demonstrate their effectiveness. In addition, the original ZNN (OZNN) and integral enhanced ZNN (IEZNN) models are used for comparison through this problem. Simulation results are consistent with the proposed theorems which validate proposed models.