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

• Published in: IEEE transactions on automatic control Vol. 68; no. 1; pp. 620 - 627
• Main Authors: Jin, Long, Wei, Lin, Li, Shuai
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Computational modeling; Convergence; Data compression and reconstruction; Differential equations; IEC Standards; inequality and equality constraints (IEC); Linear equations; Linear functions; Mathematical models; Model accuracy; Motion planning; Neural networks; Optimization; Planning; Robot dynamics; solution error; Time dependence; time-dependent nonlinear optimization (TDNO)
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2022.3144135

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.