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Optimal synthesis in the time minimization problem under phase constraints

V. V. Aleksandrov^a, A. D. Belen'kii^b, A. V. Lebedev^a, E. Matlalcuatzi Rugerio<sup>c

a</sup> Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b All-Russian Scientific Research Institute of Electromechanics
^c Benemérita Universidad Autónoma de Puebla, Mexico

Abstract: The time minimization problem in a linear system with a scalar control under phase constraints is considered. This problem is reduced to the problem of maximal deviations. Necessary conditions of control optimality are obtained. The results are applied to the problem of uniaxial stabilization of a satellite in the presence of a gravitational torque. The stabilization is performed by a flywheel engine with a limited angular momentum.

Key words: time minimization problem, phase constraints, satellite stabilization.

UDC: 517.977.55

Received: 10.06.2011

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2012, 67:1, 23–27

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