A Cerebellar Model Articulation Controller Enhanced Neural Solution to Time-Varying Linear Equations With Robotic Application

Time-varying linear equations (TVLEs) are common in practice. The existing TVLE solvers like the gradient-dynamics based neurodynamic networks (GDNNs) unavoidably introduce inevitable errors. In contrast, Getz-Marsden dynamic inverters (GMDIs) and error-dynamics based neurodynamic networks (EDNNs) require time derivatives of the coefficients and matrix inversion. To circumvent these limitations, a cerebellar model articulation controller (CMAC) enhanced GDNN (CMAC-GDNN) is proposed, where CMAC serves as a derivative estimator inspired by the fine-tuning correction mechanism for motion signals of the cerebellum. The CMAC-GDNN solver integrates GDNN and CMAC models that generate approximate solutions and correction signals, respectively. The CMAC-GDNN solver possesses some advantages of GMDI and EDNN solvers, avoiding complexities associated with the time derivatives and matrix inversion. In this paper, the structure of the CMAC-GDNN solver is presented in detail with its effectiveness and practicality demonstrated through a numerical example and a motion planning task in which a robot tracks a specific path.