Recursive Identification of Time-Varying Hammerstein Systems With Matrix Forgetting

• 成果类型: Article
• 署名作者: Dokoupil, Jakub; Vaclavek, Pavel
• 署名单位: Brno University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3188478
• 发表日期: 2023
• 页码: 3078-3085
• 关键词: estimation; Symmetric matrices; Probability density function; Parametric statistics; Bayes methods; Time-varying systems; Covariance matrices; Hammerstein model; matrix forgetting factor; Parameter Estimation; Variational Bayes

摘要

The real-time estimation of the time-varying Hammerstein system by using a noniterative learning schema is considered and extended to incorporate a matrix forgetting factor. The estimation is cast in a variational-Bayes framework to best emulate the original posterior distribution of the parameters within the set of distributions with feasible moments. The recursive concept we propose approximates the exact posterior comprising undistorted information about the estimated parameters. In many practical settings, the incomplete model of parameter variations is compensated by forgetting of obsolete information. As a rule, the forgetting operation is initiated by the inclusion of an appropriate prediction alternative into the time update. It is shown that the careful formulation of the prediction alternative, which relies on Bayesian conditioning, results in partial forgetting. This article inspects two options with respect to the order of the conditioning in the posterior, which proves vital in the successful localization of the source of inconsistency in the data-generating process. The geometric mean of the discussed alternatives then modifies recursive learning through the matrix forgetting factor. We adopt the decision-making approach to revisit the posterior uncertainty by dynamically allocating the probability to each of the prediction alternatives to be combined.