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Completeness of Riemannian metrics: an application to the control of constrained mechanical systems (2311.14969v1)

Published 25 Nov 2023 in eess.SY, cs.SY, math.DG, and math.DS

Abstract: We introduce a mathematical technique based on modifying a given Riemannian metric and we investigate its applicability to controlling and stabilizing constrained mechanical systems. In essence our result is based on the construction of a complete Riemannian metric in the modified space where the constraint is included. In particular this can be applied to the controlled Lagrangians technique Bloch et al. [2000b, 2001] modifying its metric to additionally cover mechanical systems with configuration constraints via control. The technique used consists of approximating incomplete Riemannian metrics by complete ones, modifying the evolution near a boundary and finding a controller satisfying a given design criterion.

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