Robust H_∞ gain neuro-adaptive observer design for nonlinear uncertain systems

Abstract

To guarantee convergent state estimates and exact approximations, it is highly desirable that observers can independently dominate the effects of unmodelled dynamics. Based on adaptive nonlinear approximation, this paper presents a robust H∞ gain neuro-adaptive observer (RH∞GNAO) design methodology for a large class of uncertain nonlinear systems in the presence of time-varying unknown parameters with bounded external disturbances on the state vector and on the output of the original system. The proposed RH∞GNAO incorporates radial basis function neural networks (RBFNNs) to approximate the unknown nonlinearities in the uncertain system. The weight dynamics of every RBFNN are adjusted online by using an adaptive projection algorithm. The asymptotic convergence of the state and parameter estimation errors is achieved by using Lyapunov cogitation under a well-defined persistent excitation condition, and without recourse to the strictly positive real condition. The repercussions of unknown disturbances are reduced by integrating an H∞ gain performance criterion into the proposed estimation approach. The condition imposed by this proposed observer approach, such that all estimated signals are uniformly ultimately bounded, is expressed in the form of the linear matrix inequality problem and warrants the demanded performances. To evaluate the performance of the proposed observer, various simulations are presented.