Geodesic
Stabilization of Hamiltonian systems with a guaranteed estimate of quality of management
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 7 (2014), pp. 32-44

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Stabilization problem with guaranteed estimate of quality of management of zero solution of nonautonomous Hamiltonian system was solved. It arises from the problem of optimal stabilization by reducing functional requirements for a estimate: instead of minimizing it is only necessary that it excelled to a pre-assessment. The solution is obtained by means of synthesis of active program control, acting to the system, and stabilizing control of feedback. The problem is solved analytically by the direct method of Lyapunov's stability theory with Lyapunov's function with constant sign derivatives. As examples, problems of synthesis and stabilization of program motions of homogeneous rod of variable length and variable-length pendulum in a rotating plane are solved.
Keywords: Hamiltonian system, stabilization, guaranteed estimate, quality, management, rod, pendulum, variable length. 
@article{VSGU_2014_7_a2,
     author = {E. V. Kurkina},
     title = {Stabilization of {Hamiltonian} systems with a guaranteed estimate of quality of management},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {32--44},
     publisher = {mathdoc},
     number = {7},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2014_7_a2/}
}
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E. V. Kurkina. Stabilization of Hamiltonian systems with a guaranteed estimate of quality of management. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 7 (2014), pp. 32-44. http://geodesic.mathdoc.fr/item/VSGU_2014_7_a2/