MGRNN for dynamic constrained quadratic programming with verification and applications

Abstract

Dynamic Constrained Quadratic Programming (DCQP) is at the core of problems such as portfolio optimization and robot control. However, for this dynamic problem, the Gradient Recurrent Neural Network (GRNN) suffers lag errors and the Zeroing Neural Network (ZNN) requires costly matrix inversion and derivative information. Therefore, this paper proposes a Modified Gradient Recurrent Neural Network (MGRNN) to address these limitations. Its core adaptive mechanism that retains the simplicity of explicit dynamic structure while eliminating dependencies on matrix inversion and derivative computation, thereby resolving lag errors. Moreover, theoretical analyses demonstrate that the MGRNN achieves finite-time convergence and exhibits robust performance. Besides, performance analysis validates that the MGRNN outperforms traditional GRNN by significantly reducing residuals in solving the DCQP problem. Moreover, noise tolerance experiments reveal that the MGRNN also delivers the smallest residuals and the fastest convergence among all compared models under bounded noise, confirming its superior robustness. Furthermore, its efficacy and practicality are verified through current computation in dynamic circuits with temperature-dependent resistors, as well as through applications to portfolio optimization and manipulator control. Consequently, these results collectively highlight the effectiveness and practicality of MGRNN in addressing dynamic optimization tasks, providing a robust and computationally lightweight solution for real-time applications.