Improving the transient response in backstepping control designs: Application to robotic manipulators

This paper investigates the problem of practical finite-time trajectory tracking and practical finite-time stabilization of two important classes of dynamical systems by means of C^(∞) feedbacks. It is shown that Hamiltonian mechanical systems and systems in strict feedback form can be made globally finite-time stable by smooth parameterized feedbacks. We show that we could bring all the trajectories of the closed-loop system to a small neighborhood of the origin in finite time and without peaking. Quantification of the settling time is also given in terms of two design parameters. Illustrative examples are provided to illustrate the proposed control design.