Solution concepts for linear piecewise affine differential-algebraic equations - INRIA - Institut National de Recherche en Informatique et en Automatique
Conference Papers Year : 2024

Solution concepts for linear piecewise affine differential-algebraic equations

Abstract

In this paper, we introduce a definition of solutions for linear piecewise affine differential-algebraic equations (PWA-DAEs). Firstly, to address the conflict between projectorbased jump rule and active regions, we propose a concept called state-dependent jump path. Unlike the conventional perspective that treats jumps as discrete-time dynamics, we interpret them as continuous dynamics, parameterized by a virtual timevariable. Secondly, by adapting the hybrid time-domain solution theory for continuous-discrete hybrid systems, we define the concept of jump-flow solutions for PWA-DAEs with the help of Filippov solutions for differential inclusions. Subsequently, we study various boundary behaviors of jump-flow solutions. Finally, we apply the proposed solution concepts in simulating a state-dependent switching circuit.
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hal-04707870 , version 1 (24-09-2024)

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  • HAL Id : hal-04707870 , version 1

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Yahao Chen, Stephan Trenn. Solution concepts for linear piecewise affine differential-algebraic equations. CDC 2024 - 63rd IEEE Conference on Decision and Control, Dec 2024, Milan, Italy. pp.1-6. ⟨hal-04707870⟩
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