In this work, we discuss some theoretical and numerical aspects of solving differential equations with discontinuous right-hand sides of Filippov type. In particular, (i) we propose second order corrections to the theory of Filippov, (ii) we provide a systematic and nonambiguous way to define the vector field on the intersection of several surfaces of discontinuity, and (iii) we propose, and implement, a numerical method to approximate a trajectory of systems with discontinuous right-hand sides and illustrate its performance on a few examples.

Sliding Motion in Filippov Differential Systems: Theoretical Results and a Computational Approach

LOPEZ, Luciano
2009

Abstract

In this work, we discuss some theoretical and numerical aspects of solving differential equations with discontinuous right-hand sides of Filippov type. In particular, (i) we propose second order corrections to the theory of Filippov, (ii) we provide a systematic and nonambiguous way to define the vector field on the intersection of several surfaces of discontinuity, and (iii) we propose, and implement, a numerical method to approximate a trajectory of systems with discontinuous right-hand sides and illustrate its performance on a few examples.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/11831
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