Finite-time attractivity of manifold based immersion and invariance control for inertia-wheel pendulum system

A constructive approach to design asymptotically stabilizing control laws for an inertia-wheel pendulum system is presented in this paper. The control scheme is based on immersion and invariance(I&I) which is derived starting from the selection of a target dynamical system. The process that the off-the-manifold variable converges to the origin in finite time has been strictly ensured by the proposed stabilizing control laws. A detailed stability proof and analysis is provided for the resulting closed-loop system, and the computation for the finite time is also shown as an important contribution of this work. Moreover, a saturation function is employed to update the control laws, which is effective for reducing the manifold chattering. The validity of the obtained control method is illustrated via various simulations.