Fluid dynamical systems as Hamiltonian boundary control systems

A.J. Van der Schaft, B.M. Maschke
Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)  
Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Schaft, A. Abstract It is shown how the geometric framework for dismbutedparameter port-controlled Hamiltonian systems as recently provided in [ll, 121 can be adapted to formulate ideal isentropic compressible fluids with non-zero energy flow through the boundary of the spatial domain as Hamiltonian boundary control systems. The key ingredient is the modification of the Stokes-Dirac
more » ... Stokes-Dirac structure introduced in Ill] to a Dirac structure defined on the space of mass density 3-forms and velocity I-forms, incorporating threedimensional convection. Some initial steps towards stabilization of these boundary control systems, based on the generation of Casimir functions for the closed-loop Hamiltonian system, are discussed.
doi:10.1109/.2001.980911 fatcat:2w2ee3nslba6tolnfta5rozp5a