Three types of high-order system models with parametric uncertainties are introduced, namely, the high-order fully actuated (HOFA) models, and the second- and high-order strict-feedback system (SFS) models, which possess a common full-actuation structure. Direct design approaches of adaptive stabilising controllers and adaptive tracking controllers of the HOFA models are firstly proposed based on the Lyapunov stability theory. Using the obtained result, direct second- and high-order backstepping methods for the designs of adaptive stabilising controllers of the second- and high-order SFSs with parametric uncertainties are also proposed. These approaches do not need to convert the high-order systems into first-order ones, and are thus more direct and effective. Furthermore, for a specific second- or higher-order SFS, applications of the proposed high-order backstepping methods need fewer steps than the usual first-order backstepping method, hence save much design and computation complexity.

引入了三种具有参数不确定性的高阶系统模型，即高阶完全激励（HOFA）模型，具有通用全域激励的二阶和高阶严格反馈系统（SFS）模型。致动结构。首先基于Lyapunov稳定性理论，提出了HOFA模型的自适应稳定控制器和自适应跟踪控制器的直接设计方法。利用获得的结果，还提出了直接的二阶和高阶反演方法，用于具有参数不确定性的二阶和高阶SFS的自适应稳定控制器的设计。这些方法不需要将高阶系统转换为一阶系统，因此更加直接和有效。此外，对于特定的二阶或更高阶SFS，