We consider the concept of Stokes-Dirac structures in boundary control theory proposed by van der Schaft and Maschke. We introduce Poisson reduction in this context and show how Stokes-Dirac structures can be derived through symmetry reduction from a canonical Dirac structure on the unreduced phase space. In this way, …
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8 results for “Stokes-Dirac”
Stokes-Dirac structures are infinite-dimensional Dirac structures defined in terms of differential forms on a smooth manifold with boundary. These Dirac structures lay down a geometric framework for the formulation of Hamiltonian systems with a nonzero boundary energy flow. Simplicial triangulation of the underlaying m…
This paper clarifies a global structure of Stokes-Dirac structures used for describing interconnected port-Hamiltonian systems defined on manifolds with non-trivial topology under consistent boundary condition.
Paper develops a new fluid flow model with energy exchange through boundaries.
problem Modeling ideal fluid flow with energy exchange through boundaries.
method Port-Hamiltonian model based on Stokes-Dirac structures.
result Wide range of fluid dynamical systems can be achieved with this model.
Port-Hamiltonian Modeling of Ideal Fluid Flow: Part II. Compressible and Incompressible Flowphysics.flu-dyn
Paper extends port-Hamiltonian model to include internal energy for compressible and incompressible flow.
problem Modeling fluid flow dynamics with internal energy and constraints.
method Derived port-Hamiltonian model using interconnection maps and added internal energy and constraint forces.
result Model accurately represents both compressible and incompressible fluid flow.
On the port-Hamiltonian representation of systems described by partial differential equationsmath.OC
We consider infinite dimensional port-Hamiltonian systems. Based on a power balance relation we introduce the port-Hamiltonian system representation where we pay attention to two different scenarios, namely the non-differential operator case and the differential operator case regarding the structural mapping, the dissi…
This paper focuses on the port-Hamiltonian formulation of systems described by partial differential equations. Based on a variational principle we derive the equations of motion as well as the boundary conditions in the well-known Lagrangian framework. Then it is of interest to reformulate the equations of motion in a …
Energy-Based In-Domain Control and Observer Design for Infinite-Dimensional Port-Hamiltonian Systemsmath.OC
Paper designs energy-based controllers and observers for complex systems.
problem Controlling and observing infinite-dimensional systems with in-domain actuation.
method Uses Stokes-Dirac structures and jet-bundle structures to derive controllers and observers.
result Control schemes derived in both frameworks are equivalent.