Hamiltonian Realizations of Nonlinear Adjoint Operators

Kenji Fujimoto, Jacquelien M.A. Scherpen, W. Steven Gray

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Abstract

This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel operators, and controllability and observability functions will be derived based on it. Furthermore a duality between the controllability and observability functions will be proven. The state-space realizations of such operators provide new insights to nonlinear control systems theory.
Original languageEnglish
Title of host publicationProc. IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control
PublisherUniversity of Groningen, Research Institute of Technology and Management
Number of pages7
Publication statusPublished - 2000
EventProc. IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Princeton, USA -
Duration: 1-Jan-2000 → …

Conference

ConferenceProc. IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Princeton, USA
Period01/01/2000 → …

Keywords

  • Legendre transformations
  • Hamiltonian extensions
  • Hamiltonian control systems
  • Adjoint operators
  • Nonlinear control systems

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