A novel recursive learning identification scheme for Box–Jenkins model based on error data

In this paper, a recursive learning identification scheme is proposed to estimate the parameters of the Box–Jenkins model, which is obtained by designing a new cost function. To facilitate the establishment of the new cost function, the Box–Jenkins model is transformed into an output error model through the usage of the polynomial transformation. Then, the cost function is developed based on the system output error information and the initial parameter error information, in which the output error information is introduced to raise the robustness of the identifier, and the initial parameter error information is presented to improve the convergence rate of the estimation scheme. Under the fresh framework, a novel recursive learning adaptive law can be obtained. Compared with the frequently-used loss function, the proposed algorithm provides a better estimation performance. Furthermore, under the persistent excitation condition, the estimation error can converge to zero. Finally, numerical examples and experiment are used to verify the effectiveness and usefulness of the presented algorithm.