Robust adaptive gain neural observer for a class of non‐linear systems

Abstract

This study investigates the design of robust adaptive H ∞ gain neural observer (RA H ∞ NO) for a large class of non-linear systems with unknown constant parameters in the presence of bounded external perturbations on the state vector and on the output of the original system. The proposed adaptive observer incorporates radial basis functions (RBFs) neural networks (NN) to approximate the unknown non-linearities existing in the system. The weight dynamics of every RBFNN are adjusted on-line by using an adaptive projection algorithm. The proof of the asymptotic convergence of the state and parameter estimate errors is achieved by using Lyapunov arguments under a well-defined persistent exciting condition, and without recourse to the strictly positive real condition. The effect of unknown disturbances is reduced by integrating a H ∞ gain performance criterion into the proposed estimation scheme. The existence condition of the proposed observer such that all estimated signals are uniformly ultimately bounded is expressed in the form of the linear matrix inequality problem. To evaluate the performance of the proposed observer, three simulations are made.