Gradient-Based Differential Neural-Solution to Time-Dependent Nonlinear Optimization

• 成果类型: Article
• 署名作者: Jin, Long; Wei, Lin; Li, Shuai
• 署名单位: Lanzhou University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3144135
• 发表日期: 2023
• 页码: 620-627
• 关键词: Data compression and reconstruction; inequality and equality constraints (IEC); solution error; time-dependent nonlinear optimization (TDNO)

摘要

In this technical article, to seek the optimal solution to time-dependent nonlinear optimization subject to linear inequality and equality constraints (TDNO-IEC), the gradient-based differential neural-solution, termed as GDN model, is proposed and researched. Notably, TDNO-IEC is first converted into the nonhomogeneous linear equation with the dynamic parameter. Second, differential neural-solution with the aid of gradient is designed. The contrastive theoretical analyses among the GDN model, gradient-based neural network (GNN), and the dual neural network (DNN) prove that the proposed GDN model has higher accuracy for eliminating the large solution error with exponential convergence. In addition, reasonable convergent time of the GDN model is guaranteed by activation functions with simple formulation. Last, an illustrative example and real-world applications, including robot motion planning and data dimension reduction and reconstruction, further validate the high availability of the proposed GDN model.