Differential algebraic system nodes
Mehmet Erbay, Birgit Jacob, Timo Reis
TL;DR
This paper extends the theory of infinite-dimensional differential algebraic equations by introducing operator and system nodes that incorporate algebraic constraints, and applies this to port-Hamiltonian DAEs.
Contribution
It develops a framework for differential-algebraic systems with algebraic constraints using operator and system nodes, and characterizes solutions via extrapolation spaces and Wong sequences.
Findings
Extended operator and system nodes to include algebraic constraints.
Characterized solutions of extrapolated DAEs using Wong sequences.
Applied the theory to infinite-dimensional port-Hamiltonian DAEs.
Abstract
Infinite-dimensional differential algebraic equations (short DAEs) with input and output are studied. The concepts of operator nodes and system nodes are extended to systems which additionally may include algebraic constraints. Extrapolation spaces are investigated for differential-algebraic equations, and solutions of the extrapolated DAE are characterized using augmented Wong sequences. The resulting theory is then applied to characterize infinite-dimensional port-Hamiltonian DAEs.
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Taxonomy
TopicsControl and Stability of Dynamical Systems · Numerical methods for differential equations · Polynomial and algebraic computation