Adaptive stochastic tracking: DNN-approach

A class of uncertain nonlinear stochastic processes, satisfying a "globally Lipschitz-type strip condition" and supplied by a linear output equation, is considered. The problem of a robust nonlinear tracking controller design is tackled. It consists of the construction of an adaptive robust controller which guarantees the joint performance for the given class of uncertain stochastic systems using the online state estimates. These estimates are suggested to be obtained by a dynamic neural network (DNN) approach. A new type of differential learning law for the weight dynamics is applied. By the stochastic Lyapunov-like analysis (with Ito formula implementation), the stability conditions for such adaptive controller (including the state estimation) are established. The upper bound for the tracking error is derived. A numerical example, dealing with "module" type nonlinearities, illustrates the effectiveness of the suggested approach.