Passivity-Based Observer Design for a Class of Lagrangian Systems with Perfect Unilateral Constraints

Aneel Tanwani 1 Bernard Brogliato 1, * Christophe Prieur 2
* Corresponding author
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
Abstract : This paper addresses the problem of estimating the velocity variables, using the position measurement as output, in nonlinear Lagrangian dynamical systems with perfect unilateral constraints. The dynamics of such systems are formulated as a measure differential inclusion (MDI) at velocity level which naturally encodes the relations for prescribing the post-impact velocity. Under the assumption that the velocity of the system is uniformly bounded, an observer is designed which is also a measure differential inclusion. It is proved that there exists a unique solution to the proposed observer and that solution converges asymptotically to the actual velocity.
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Aneel Tanwani, Bernard Brogliato, Christophe Prieur. Passivity-Based Observer Design for a Class of Lagrangian Systems with Perfect Unilateral Constraints. 52nd IEEE Conference on Decision and Control (CDC 2013), Dec 2013, Florence, Italy. pp.3338-3343, ⟨10.1109/CDC.2013.6760393⟩. ⟨hal-00908734⟩

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