Immersion and invariance adaptive finite-time stabilization of high-order systems

The design of a novel adaptive finite-time stable control system for high-order systems with parameter uncertainties is presented. Specified dynamics with recursive structure is employed as the finite-time convergent target system, thus leading to a systematic design process for systems with arbitrary order. Estimators for unknown parameters are constructed using immersion and invariance (I&I) theory. Benefiting from the flexibility of I&I-based estimator design, a complete finite-time stability analysis of the closed-loop system is presented using finite-time Lyapunov function technique. Particularly, the results stated here avoid the need of any polynomial conditions proposed in the previous works. Much improved performance of the proposed control scheme is also demonstrated using various numerical examples.