Real-Time Solutions for Dynamic Complex Matrix Inversion and Chaotic Control Using ODE-Based Neural Computing Methods

This paper proposes a robust dual-integral structure zeroing neural network (ZNN) design framework, effectively overcoming the limitations of existing single-integral enhanced ZNN models in completely suppressing linear noise. Based on this design framework, a complex-type dual-integral structure ZNN (DISZNN) model with inherent linear noise suppression capability is constructed for computing dynamic complex matrix inversion (DCMI) online. The stability, convergence, and robustness of the proposed DISZNN model are ensured via rigorous theoretical analyses. In three distinct experiments involving DCMI (including cases with only imaginary parts, both real and imaginary parts, and high-dimensional scenarios), the state trajectories of the DISZNN model are well and quickly fitted to the dynamic trajectories of the theoretical solutions with very low residual errors in various linear noise environments. More specifically, the residual errors of the DISZNN model for online computation of DCMI under linear noise environments are consistently below the order of $10^{-3}$, representing one-thousandth of the residual errors in existing noise-tolerant ZNN models. Finally, the DISZNN design framework is applied to construct a controlled chaotic system of a permanent magnet synchronous motor (PMSM) with uncertainties and external disturbances based on real-world modeling. Experimental results demonstrate that the three state errors of the controlled PMSM chaotic system converge to zero quickly and stably under various conditions (system parameters, external disturbances, and uncertainties), further highlighting the superiority and generalizability of the DISZNN design framework.