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Numerical integration of hybrid dynamical systems via domain relaxation

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5 Author(s)
Sam Burden ; Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, 94720, USA ; Humberto Gonzalez ; Ram Vasudevan ; Ruzena Bajcsy
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Though hybrid dynamical systems are a powerful modeling tool, it has proven difficult to accurately simulate their trajectories. In this paper, we develop a provably convergent numerical integration scheme for approximating trajectories of hybrid dynamical systems. This is accomplished by first relaxing hybrid systems whose continuous states reside on manifolds by attaching epsilon-sized strips to portions of the boundary and then extending the dynamic and distance metric onto these strips. On this space we develop a numerical integration scheme and prove that discrete approximations converge to trajectories of the hybrid system. An example is included to illustrate the approach.

Published in:

2011 50th IEEE Conference on Decision and Control and European Control Conference

Date of Conference:

12-15 Dec. 2011