The main goal of this paper is to design a state feedback control that makes a point mass track a non-Zeno reference trajectory in a planar billiard. This objective is achieved by first determining a continuous-time dynamical model, whose trajectories approximate the solutions of the hybrid system. Hence, a state feedback that makes the hybrid system track a reference trajectory of the continuous-time one is proposed. Finally, these two techniques are combined in order to find a state feedback that achieves tracking of the trajectories of the unforced system. Examples are reported all throughout the paper to illustrate the theoretical results.
Tracking of a Bouncing Ball in a Planar Billiard Through Continuous-Time Approximations
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 14, 2017; final manuscript received March 26, 2018; published online April 27, 2018. Assoc. Editor: Bernard Brogliato.
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Menini, L., Possieri, C., and Tornambè, A. (April 27, 2018). "Tracking of a Bouncing Ball in a Planar Billiard Through Continuous-Time Approximations." ASME. J. Comput. Nonlinear Dynam. June 2018; 13(6): 061006. https://doi.org/10.1115/1.4039876
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