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A. Macchelli, R. Pasumarthy, A. J. van der Schaft
"Control of Port Hamiltonian Systems by Interconnection and Energy Shaping via Generation of Casimir Functions. An Overview"
 
Type Conference
Author(s) A. Macchelli, R. Pasumarthy, A. J. van der Schaft
Title Control of Port Hamiltonian Systems by Interconnection and Energy Shaping via Generation of Casimir Functions. An Overview
Editor 5th MATHMOD Conference
Keywords control by interconnection, port Hamiltonian systems
Abstract
In this paper, an overview on the control by interconnection and energy shaping via Casimir generation for port Hamiltonian systems is presented. This control methodology has its origins in the Energy-Casimir method according to which stability can be proved by using in Lyapunov analysis next to system Hamiltonian other conserved quantities. In the control by interconnection, the controller structure is chosen in order to properly introduce such conserved quantities (Casimir functions) and shape the energy of the system such that a minimum in the desired equilibrium configuration can be introduced. In this paper, the basic results on the stabilization of finite dimensional system are summarized and then generalized in order to cope with distributed parameter plant. The stabilization of a set of port Hamiltonian systems interconnected by (dissipative) transmission lines is presented in order to illustrate the design methodology.
Year 2006


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