Robust high-gain DNN observer for nonlinear stochastic continuous time systems

A class of nonlinear stochastic processes, satisfying a "Lipschitz-type strip condition" and supplied by a linear output equation, is considered. Robust asymptotic (high-gain) state estimation for nonlinear stochastic processes via differential neural networks is discussed. A new type learning law for the weight dynamics is suggested. By a stochastic Lyapunov-like analysis (with Ito formula implementation), the stability conditions for the state estimation error as well as for the neural network weights are established. The upper bound for this error is derived. The numerical example, dealing with "module"-type nonlinearities, illustrates the effectiveness of the suggested approach.