Hamiltonian realizations of nonlinear adjoint operators

This paper addresses the issue of state-space realizations for nonlinear adjoint operators. In particular, the relationships between nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are established. Then, characterizations of the adjoints of controllability, observability and Hankel operators are derived from this analysis. The state-space realizations of such adjoint operators provide new insights on singular value analysis and duality issues in nonlinear control systems theory. Finally, a duality between the controllability and observability energy functions is proved. Key words: Nonlinear systems; State-space realization; Duality; Controllability; Observability.

• Type: Journal
• Year: 2002
• Where: AUTOMATICA
• Authors: Kenji Fujimoto, Jacquelien M. A. Scherpen, W. Steven Gray
• Keywords: Adjoint Operators, AUTOMATICA 2002, Nonlinear Adjoint Operators, State-space Realization