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| J.LorcaESPIRO,C.Mu˜nozPOBLETE |
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| (Departamento de Ciencias Fisicas, Facultad de Ingenieria, Ciencias y Administracion, Universidad de La Frontera;Departamento de Ingenieria Electrica, Facultad de Ingenieria, Ciencias y Administracion, Universidad de La Frontera) |
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| Received:April 08, 2011Revised:October 11, 2011 |
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| Symplectic feedback using Hamiltonian Lie algebra and its applications to an inverted pendulum |
| J. Lorca ESPIRO,C.Mu˜noz POBLETE |
| (Departamento de Ciencias Fisicas, Facultad de Ingenieria, Ciencias y Administracion, Universidad de La Frontera;Departamento de Ingenieria Electrica, Facultad de Ingenieria, Ciencias y Administracion, Universidad de La Frontera) |
| Abstract: |
| From the symplectic representation of an autonomous nonlinear dynamical system with holonomic constraints, i.e., those that can be represented through a symplectic form derived from a Hamiltonian, we present a new proof on the realization of the symplectic feedback action, which has several theoretical advantages in demonstrating the uniqueness and existence of this type of solution. Also, we propose a technique based on the interpretation, construction and characterization of the pull-back differential on the symplectic manifold as a member of a one-parameter Lie group. This allows one to synthesize the control law that governs a certain system to achieve a desired behavior; and the method developed from this is applied to a classical system such as the inverted pendulum. |
| Key words: Hamiltonian systems Symplectic structures Lie algebra Nonlinear dynamical systems Geometric control |
