Dynamic Moore–Penrose Inversion With Unknown Derivatives: Gradient Neural Network Approach

Finding dynamic Moore–Penrose inverses (DMPIs) in real-time is a challenging problem due to the time-varying nature of the inverse. Traditional numerical methods for static Moore–Penrose inverse are not efficient for calculating DMPIs and are restricted by serial processing. The current state-of-the-art method for finding DMPIs is called the zeroing neural network (ZNN) method, which requires that the time derivative of the associated matrix is available all the time during the solution process. However, in practice, the time derivative of the associated dynamic matrix may not be available in a real-time manner or be subject to noises caused by differentiators. In this article, we propose a novel gradient-based neural network (GNN) method for computing DMPIs, which does not need the time derivative of the associated dynamic matrix. In particular, the neural state matrix of the proposed GNN converges to the theoretical DMPI in finite time. The finite-time convergence is kept by simply setting a large parameter when there are additive noises in the implementation of the GNN model. Simulation results demonstrate the efficacy and superiority of the proposed GNN method.