Gradient-based differential neural network to time-varying constrained quadratic programming

Abstract

This paper introduces a novel approach to solving time-varying quadratic programming (TVQP) problems with time-dependent constraints, using gradient-based differential neural networks (GDNN). We establish the theoretical framework for both conventional gradient neural networks (CGNN) and GDNN models, highlighting their effectiveness in addressing dynamic optimization challenges. Comparative theoretical analyses show that the proposed GDNN model achieves higher accuracy than the CGNN model, significantly reducing solution errors with exponential convergence. Moreover, the use of a sign-bi-power activation function (SBPAF) ensures reasonable convergence times for the GDNN model. Our approach is validated through simulations of TVQP problems under specific constraints. The results demonstrate that while both models are capable of solving these problems, the GDNN model outperforms the CGNN model in minimizing optimization errors (residual errors), especially when varying the scaling factor $\gamma$, the GDNN model also shows superior performance and more efficient convergence.