Optimal synthesis in the time-minimization problem under phase constrains} / V. V. Aleksandrov, A. D. Belen'kii, A. V. Lebedev, E. Matlalcuatzi Rugerio. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. № 1. P. 67-71 [Moscow Univ. Math. Bulletin. Vol. 67, N 1, 2012.].
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.