A New Varying-Parameter Convergent-Differential Neural-Network for Solving Time-Varying Convex QP Problem Constrained by Linear-Equality

• Published in: IEEE transactions on automatic control Vol. 63; no. 12; pp. 4110 - 4125
• Main Authors: Zhang, Zhijun, Lu, Yeyun, Zheng, Lunan, Li, Shuai, Yu, Zhuliang, Li, Yuanqing
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Biological neural networks; Computer simulation; Convergence; Convergence and robustness; Design parameters; Mathematical model; Neural networks; Perturbation methods; quadratic programming; Recurrent neural networks; Robustness; time-varying
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2018.2810039

To solve online continuous time-varying convex quadratic-programming problems constrained by a time-varying linear-equality, a novel varying-parameter convergent-differential neural network (termed as VP-CDNN) is proposed and analyzed. Different from fixed-parameter convergent-differential neural network (FP-CDNN), such as the gradient-based recurrent neural network, the classic Zhang neural network (ZNN), and the finite-time ZNN (FT-ZNN), VP-CDNN is based on monotonically increasing time-varying design-parameters. Theoretical analysis proves that VP-CDNN has super exponential convergence and the residual errors of VP-CDNN converge to zero even under perturbation situations, which are both better than traditional FP-CDNN and FT-ZNN. Computer simulations based on different activation functions are illustrated to verify the super exponential convergence performance and strong robustness characteristics of the proposed VP-CDNN. A robot tracking example is finally presented to verify the effectiveness and availability of the proposed VP-CDNN.