Abstract
This article considers the numerical treatment of piecewise-smooth dynamical systems. Classical solutions as well as sliding modes up to codimension-2 are treated. An algorithm is presented that, in the case of non-uniqueness, selects a solution that is the formal limit solution of a regularized problem. The numerical solution of a regularized differential equation, which creates stiffness and often also high oscillations, is avoided.
Highlights
Piecewise-smooth dynamical systems arise in many applications and they are an active field of recent research
This article considers the numerical treatment of piecewise-smooth dynamical systems
With event detection we solve the discontinuous problem but, instead of following all solutions in the case of non-uniqueness, we propose to select the solution which can formally be interpreted as the limit solution of a regularized differential equation
Summary
Piecewise-smooth dynamical systems arise in many applications and they are an active field of recent research. With event detection we solve the discontinuous problem (without any ε) but, instead of following all solutions in the case of non-uniqueness, we propose to select the solution which can formally be interpreted as the limit solution (for ε → 0) of a regularized differential equation. This selection is partly done on the basis of the classification in [17]. The main part (Section 4) presents in an algorithmic way the switching between different kinds of solutions at the discontinuity hyper-surfaces The article finishes with some comments on the implementation (Section 6) and a conclusion (Section 7)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
