A Petrov-Galerkin discretization framework preserves discrete dissipation inequalities for a general class of energy-based models, including circuits, Cahn-Hilliard, and doubly nonlinear diffusion.
Passivity encoding representations of nonlinear systems
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abstract
Passive systems are characterized by their inability to generate energy internally, providing a powerful tool for modeling physical phenomena. Additionally, algebraically encoding passivity in the system description can be advantageous. For this, port-Hamiltonian systems are a prominent approach. Another possibility is writing the system in suitable coordinates. In this paper, we investigate the equivalence between passivity and the feasibility of passivity encoding representations, thereby elaborating upon existing results for port-Hamiltonian systems. Based on our findings, we present a method to construct port-Hamiltonian representations of a passive system if the dynamics and the Hamiltonian are known.
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Structure-Preserving Discretization and Model Reduction for Energy-Based Models
A Petrov-Galerkin discretization framework preserves discrete dissipation inequalities for a general class of energy-based models, including circuits, Cahn-Hilliard, and doubly nonlinear diffusion.