High-order fully actuated system approaches: Part IV. Adaptive control and high-order backstepping

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.