Parameter recovery of Neural Network-Based Hammerstein system via immersion and invariance adaptive optimization scheme

Abstract

Most of the established estimation techniques for nonlinear systems have been proposed by using certainty equivalence method, potentially resulting in a tricky issue. In this paper, we introduce an immersion and invariance (I&I) estimation scheme for nonlinear neural network-based Hammerstein system, where the estimation error data and non-certainty equivalence method are used. To achieve above-mentioned purpose, the estimation error information is extracted by considering some filtered regression vectors and the developed adaptive dynamic filter. Then, two auxiliary functions are proposed based on I&I theory, which are used to drive the adaptive estimator. Finally, a novel parameter estimation adaptive law with recursive gain is designed by incorporating the estimation error data, the auxiliary functions and regularisation operation. Two numerical simulations and an experiment on a servo system are conducted to illustrate the effectiveness and availability of the proposed I&I estimator.