Abstract: By using Lyapunov stability theory, an observer-based H∞ adaptive controller design method was proposed for a class of Hamiltonian systems with parametric uncertainties in this paper. First, the H∞ controller design problem was investigated for nominal Hamiltonian systems and the obtained result was extended to Hamiltonian systems with parametric uncertainties. The H∞ adaptive controller was also proposed. Next, considering the immeasurable of the system states and according to the structural characteristics of uncertain Hamilton systems, an observer-based H∞ adaptive controller design method was presented. Finally, the validity of the proposed method is verified by a numerical example.

Key words: Hamilton system, H_∞ control, observer, adaptive control

摘要： 针对一类参数不确定Hamilton系统，根据Lyapunov稳定性理论，提出一种基于观测器的 自适应控制方法。首先，针对标称Hamilton系统，研究其控制器设计问题，将结果推广至含有参数不确定性的Hamilton系统，并给出其 自适应控制器设计方法。然后，考虑到系统状态的不可测性，根据不确定Hamilton系统的结构特点，提出一种基于状态观测器的 自适应控制器设计方法。最后，通过数值仿真验证所提方法的有效性。

关键词: Hamilton系统, 控制, 观测器, 自适应控制