Dirac and Lagrange algebraic constraints in nonlinear port-Hamiltonian systems

DOI10.1007/s10013-020-00419-xzbMath1470.37083arXiv1909.07025OpenAlexW3036638511MaRDI QIDQ2022393

Bernhard Maschke, Arjan J. Van der Schaft

Publication date: 29 April 2021

Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.07025

zbMATH Keywords

nonlinear controlHamiltonian systemsdifferential-algebraic equationsLagrangian submanifoldsDirac structures

Mathematics Subject Classification ID

Nonlinear systems in control theory (93C10) Lyapunov and storage functions (93D30) Implicit ordinary differential equations, differential-algebraic equations (34A09) Dynamical systems in control (37N35) Lagrangian submanifolds; Maslov index (53D12) Constrained dynamics, Dirac's theory of constraints (70H45) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (7)

Optimal Control of Port-Hamiltonian Descriptor Systems with Minimal Energy Supply ⋮ Control of port-Hamiltonian differential-algebraic systems and applications ⋮ Differential-algebraic systems with dissipative Hamiltonian structure ⋮ Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems ⋮ Port-Hamiltonian formulations of the incompressible Euler equations with a free surface ⋮ Passivity, port-Hamiltonian formulation and solution estimates for a coupled magneto-quasistatic system ⋮ Mini-workshop: Mathematics of dissipation -- dynamics, data and control. Abstracts from the mini-workshop held May 9--15, 2021 (hybrid meeting)

Cites Work

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• Linear Algebra Properties of Dissipative Hamiltonian Descriptor Systems
• Dirac Manifolds
• Port-Hamiltonian Differential-Algebraic Systems
• Port-Hamiltonian Systems Theory: An Introductory Overview

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