A meta-interactive neural network for solving time-varying quadratic programming problems

Many practical applications can be formulated as time-varying quadratic programming (TVQP) problems. Improving solution speed and accuracy can theoretically enhance efficiency. However, existing solvers such as the zeroing neural network (ZNN) and varying-parameter recurrent neural network (VPRNN) exhibit inherent limitations. Here, we propose a meta-interactive neural network (MINN). Unlike the independent neural structures in ZNN and VPRNN, the proposed MINN constructs a coupled topology for neurons, enabling information exchange within the network, and utilizing group dynamics to accelerate the convergence process. Notably, MINN relaxes the activation function constraints imposed by ZNN, allowing the use of non-monotonically increasing odd functions, thereby broadening the class of admissible activations. Lyapunov-based analysis confirms the enhanced convergence properties of MINN. Furthermore, numerical simulations demonstrate that MINN consistently outperforms ZNN and VPRNN in terms of convergence speed and robustness. Surprisingly, MINN also generalizes well to other time-varying problems, such as the Sylvester equation. Additionally, a detailed analysis of the coupling parameters reveals its critical role in system performance. Finally, applying MINN to robotic motion planning improves control accuracy from 10^-6m to 10^-7m.