CUED Publications database

Tracking control in billiards using mirrors without smoke, Part I: Lyapunov-based local tracking in polyhedral regions

Forni, F and Teel, AR and Zaccarian, L (2011) Tracking control in billiards using mirrors without smoke, Part I: Lyapunov-based local tracking in polyhedral regions. In: UNSPECIFIED pp. 3283-3288..

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Abstract

In this paper we formulate the tracking problem of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set. Due to the discontinuous dynamics arising from nonsmooth impacts, the tracking problem is formulated within a hybrid systems framework and a Lyapunov function is given, which decreases during flow (continuous motion) and remains constant across jumps (impacts of the masses). To guarantee non-increase of the Lyapunov function at jumps, we introduce a novel concept of mirrored images of the target mass and prove that, with this concept, local tracking is achieved. Several simulations illustrate the effectiveness of the proposed approach as compared to alternative solutions. In a companion paper [6] we address global results and generalize the local approach to curved billiards. © 2011 IEEE.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Subjects: UNSPECIFIED
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:29
Last Modified: 28 Sep 2017 01:39
DOI: