Hamiltonian and self-adjoint control systems |
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| Authors: | A. van der Schaft P. E. Crouch |
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| Affiliation: | 1. Departamento de Química Biológica Ranwel Caputto, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Argentina;2. Centro de Investigaciones en Química Biológica de Córdoba, CIQUIBIC, CONICET, Universidad Nacional de Córdoba, Argentina;3. Cátedra de Química Biológica, Departamento de Química, Facultad de Ciencias Exactas, Físicas y Naturales, Universidad Nacional de Córdoba, Argentina;4. Instituto de Investigaciones Biológicas y Tecnológicas (IIBYT), CONICET, Universidad Nacional de Córdoba. Córdoba, Argentina;5. Department of Dermatology, Aalborg University Hospital, Denmark;6. Ministerio de Ciencia y Tecnología de la Provincia de Córdoba, Argentina |
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| Abstract: | This paper outlines results recently obtained in the problem of determining when an input-output map has a Hamiltonian realization. The results are obtained in terms of variations of the system trajectories, as in the solution of the Inverse Problem in Classical Mechanics. The variational and adjoint systems are introduced for any given nonlinear system, and self-adjointness defined. Under appropriate conditions self-adjointness characterizes Hamiltonian systems. A further characterization is given directly in terms of variations in the input and output trajectories, proving an earlier conjecture by the first author. |
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| Keywords: | Hamiltonian system Minimality Lagrangian submanifolds Symplectic |
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