Dirac and Lagrange algebraic constraints in nonlinear port-Hamiltonian\n systems

2019/09/16 by Arjan van der Schaft, van der Schaft, Arjan, Bernhard Maschke +1 · 5 citations
Engineering · Mathematics · #34A09 #53D12 #65L80 #70B45 #93C10 #Advanced Topics in Algebra #Control and Stability of Dynamical Systems #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1909.07025

openalex publication_date 2019/09/16 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

After recalling standard nonlinear port-Hamiltonian systems and their\nalgebraic constraint equations, called here Dirac algebraic constraints, an\nextended class of port-Hamiltonian systems is introduced. This is based on\nreplacing the Hamiltonian function by a general Lagrangian submanifold of the\ncotangent bundle of the state space manifold, motivated by developments in\nBarbero-Linan et al., and extending the linear theory as developed in Van der\nSchaft et al., Beattie et al.. The resulting new type of algebraic constraints\nequations are called Lagrange constraints. It is shown how Dirac algebraic\nconstraints can be converted into Lagrange algebraic constraints by the\nintroduction of extra state variables, and, conversely, how Lagrange algebraic\nconstraints can be converted into Dirac algebraic constraints by the use of\nMorse families.\n

Cited by

• Strong imposition of Dirichlet boundary velocities in structure-preserving discretizations of elastodynamics
• Inertia Partitioning Modular Control Framework for Reconfigurable Multibody Systems
• Weak solutions of port-Hamiltonian systems
• Structure-Preserving Discretization and Model Reduction for Energy-Based Models
• Structure-preserving space discretization of differential and nonlocal constitutive relations for port-Hamiltonian systems

Related

• Generalized Port-Hamiltonian DAE Systems
• Port-Hamiltonian systems with energy and power ports
• Linear port-Hamiltonian DAE systems revisited
• Stokes-Lagrange and Stokes-Dirac representations of N-dimensional port-Hamiltonian systems for modelling and control
• Discretization of Dirac systems and port-Hamiltonian systems: the role of the constraint algorithm