Zhang neural network versus gradient-based neural network for time-varying linear matrix equation solving

摘要

A type of recurrent neural networks called Zhang neural network (ZNN) is presented and investigated to provide an online solution to the time-varying linear matrix equation, A(t)X(t)B(r)+X(t) = C(t) by using a novel design method. In contrast to the gradient-based neural network (GNN), the novel design of ZNN is based on a matrix-valued indefinite error function, instead of a scalar-valued norm-based energy function. Therefore, a ZNN model depicted in implicit dynamics can globally and exponentially converge to the time-varying theoretical solution of the given linear matrix equation. Computer simulation results further demonstrate the superior performance of the ZNN model in solving the time-varying linear matrix equation compared with the conventional GNN model.