Local-homogeneity-based global continuous control for mechanical systems with constrained inputs: finite-time and exponential stabilisation

"A global continuous control scheme for the finite-time or (local) exponential stabilisation of mechanical systems with constrained inputs is proposed. The approach is formally developed within the theoretical framework of local homogeneity. This has permitted to solve the formulated problem not only guaranteeing input saturation avoidance but also giving a wide range of design flexibility. The proposed scheme is characterised by a saturating-proportional-derivative type term with generalised saturating and locally homogeneous structure that permits multiple design choices on both aspects. The work includes a simulation implementation section where the veracity of the so-cited argument claiming that finite-time stabilisers are faster than asymptotical ones is studied. In particular, a way to carry out the design so as to, indeed, guarantee faster stabilisation through finite-time controllers (beyond their finite-time convergence) is shown.

Global finite-time stability characterized through a local notion of homogeneity

"In this work, a notion of local homogeneity is formally defined. Important results involving homogeneous functions or vector fields are reformulated in the consequent local context. In particular, global finite-time stability is characterized through the proposed notion of local homogeneity. As an application of the developed analytical setting, a global finite-time stabilization scheme for robot manipulators with bounded inputs is presented. The developed framework and results prove to be useful to relax analytical and synthesis constraints imposed or generated by homogeneity requirements.