Complex-Valued Discrete-Time Neural Dynamics for Perturbed Time-Dependent Complex Quadratic Programming With Applications

• Published in: IEEE transaction on neural networks and learning systems Vol. 31; no. 9; pp. 3555 - 3569
• Main Authors: Qi, Yimeng, Jin, Long, Wang, Yaonan, Xiao, Lin, Zhang, Jiliang
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.09.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Complex domain; Computational modeling; Computer applications; Computer simulation; Constraint modelling; Convergence; Cybernetics; discrete-time neural dynamics (DTND); Internet; Mathematical model; Mathematical models; Model accuracy; Neural networks; Numerical models; Perturbation methods; Quadratic programming; quadratic programming (QP); quasi-Newton Broyden–Fletcher–Goldfarb–Shanno (BFGS); Recurrent neural networks; Robotics; Robots; Robustness (mathematics); Time dependence
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2019.2944992

It has been reported that some specially designed recurrent neural networks and their related neural dynamics are efficient for solving quadratic programming (QP) problems in the real domain. A complex-valued QP problem is generated if its variable vector is composed of the magnitude and phase information, which is often depicted in a time-dependent form. Given the important role that complex-valued problems play in cybernetics and engineering, computational models with high accuracy and strong robustness are urgently needed, especially for time-dependent problems. However, the research on the online solution of time-dependent complex-valued problems has been much less investigated compared to time-dependent real-valued problems. In this article, to solve the online time-dependent complex-valued QP problems subject to linear constraints, two new discrete-time neural dynamics models, which can achieve global convergence performance in the presence of perturbations with the provided theoretical analyses, are proposed and investigated. In addition, the second proposed model is developed to eliminate the operation of explicit matrix inversion by introducing the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Moreover, computer simulation results and applications in robotics and filters are provided to illustrate the feasibility and superiority of the proposed models in comparison with the existing solutions.