TY - JOUR
T1 - Differential Equivalence for Linear Differential Algebraic Equations
AU - Tognazzi, Stefano
AU - Tribastone, Mirco
AU - Tschaikowski, Max
AU - Vandin, Andrea
PY - 2022/7
Y1 - 2022/7
N2 - Differential-algebraic equations (DAEs) are a widespread dynamical model that describes continuously evolving quantities defined with differential equations, subject to constraints expressed through algebraic relationships. As such, DAEs arise in many fields ranging from physics, chemistry, and engineering. In this paper we focus on linear DAEs, and develop a theory for their minimization up to an equivalence relation. We present differential equivalence, which relates DAE variables that have equal solutions at all time points (thus requiring them to start with equal initial conditions) and extends the line of research on bisimulations developed for Markov chains and ordinary differential equations. We apply our results to the electrical engineering domain, showing that differential equivalence can explain invariances in certain networks as well as analyze DAEs which could not be originally treated due to their size.
AB - Differential-algebraic equations (DAEs) are a widespread dynamical model that describes continuously evolving quantities defined with differential equations, subject to constraints expressed through algebraic relationships. As such, DAEs arise in many fields ranging from physics, chemistry, and engineering. In this paper we focus on linear DAEs, and develop a theory for their minimization up to an equivalence relation. We present differential equivalence, which relates DAE variables that have equal solutions at all time points (thus requiring them to start with equal initial conditions) and extends the line of research on bisimulations developed for Markov chains and ordinary differential equations. We apply our results to the electrical engineering domain, showing that differential equivalence can explain invariances in certain networks as well as analyze DAEs which could not be originally treated due to their size.
U2 - 10.1109/TAC.2021.3108530
DO - 10.1109/TAC.2021.3108530
M3 - Journal article
SN - 0018-9286
VL - 67
SP - 3484 3493
JO - I E E E Transactions on Automatic Control
JF - I E E E Transactions on Automatic Control
IS - 7
ER -