Least-Squares Model-Reference Adaptive Control: Extension to Higher Relative Degree Plants

• 成果类型: Article
• 署名作者: Costa, Ramon R.
• 署名单位: Universidade Federal Rural do Rio de Janeiro (UFRRJ); Universidade Federal do Rio de Janeiro
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2026.3674420
• 发表日期: 2026
• 关键词: design

摘要

A Lyapunov-based least-squares model-reference adaptive controller was recently developed for plants with relative degree one. The algorithm exhibits a remarkable tracking error transient performance while also ensuring fast parameter convergence. In this article, we generalize this algorithm to the more complex and challenging case of plants with higher relative degree. The key elements for the design procedure are the strictly positive real (SPR) principle and the backstepping technique. The idea here is to employ the backstepping technique to retrieve the control law from its filtered signal. This solution, however, requires the derivative of the tracking error, which is provided by a first-order passive observer. The SPR principle, so fundamental to the controller design, is also exploited in the observer design. The proposed SPR observer is the key to replicating the analysis performed for the controller. As a result, least-squares update laws can be employed for both.