An improving integration-enhanced ZNN for solving time-varying polytope distance problems with inequality constraint

Time-varying polytope distance (TVPD) problems are prevalent in scientific and engineering applications and can be transformed into time-varying quadratic programming (TVQP) problems with both equality and inequality constraints. Concurrently, the noise interferences during the solution process are non-negligible and challenging to eliminate. Although zeroing neural networks (ZNNs) perform well in solving various types of time-varying problems, they still fall short in the suppression of unbounded noises, such as linear noise. To address this limitation, this paper proposes an improving integration-enhanced ZNN (IIEZNN) model for accurately solving TVPD problems under noise environments. Compared with the existing ZNN models, the IIEZNN model has stronger inherent robustness. The stability and robustness of the IIEZNN model are guaranteed by rigorous theoretical analysis. Firstly, the effectiveness of the IIEZNN model is verified via two TVQP examples. Then, the IIEZNN model is generalized to TVPD problem solving and has excellent performance. Specifically, in solving the TVPD under linear noises, the residual error of the IIEZNN model converges to the order of \(10^{-5}\) ${10}^{-5}$ , which is much lower than that of the existing noise-tolerant ZNN model with an order of \(10^{-1}\) ${10}^{-1}$ .