Hamiltonian Systems as Passive Systems
Authors
Abstract
In this chapter we deal with Euler-Lagrange and Hamiltonian systems as an important class of passive state space systems. First we consider the passivity of systems described by Euler-Lagrange equations, with an application to a tracking problem. We define the class of port-controlled Hamiltonian systems, including the examples of LC-circuits and mechanical systems with kinematic constraints. This framework is further extended to include dissipation. Stabilization procedures for port-controlled Hamiltonian systems, which exploit the Hamiltonian structure and the passivity property, are discussed. Finally, the notion of power-conserving interconnection is formalized, leading to the notion of implicit port-controlled Hamiltonian systems.
Keywords
Hamiltonian System; Kinematic Constraint; Passive System; Storage Function; Dirac Structure
Citation
- ISBN: 9781447111542
- Publisher: Springer London
- DOI: 10.1007/978-1-4471-0507-7_4
BibTeX
@inbook{van_der_Schaft_2000,
title={{Hamiltonian Systems as Passive Systems}},
ISBN={9781447105077},
ISSN={0178-5354},
DOI={10.1007/978-1-4471-0507-7_4},
booktitle={{L2 - Gain and Passivity Techniques in Nonlinear Control}},
publisher={Springer London},
author={van der Schaft, Arjan},
year={2000},
pages={63--123}
}