A. G. Nagiev1, F. B. Imranov2, and G. A. Nagiev2
1Sumgayit State University, kvartal 43, Sumgayit, Azerbaijan
E-mail: nashfn@hotbox.ru
2Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences,
ul. F. Agaeva 9, Baku, 370141 Azerbaijan
Received July 23, 2010; in final form, November 12, 2010
Abstract—The problem of predictor–corrector control of nonlinear dynamic systems based on a pre-
liminarily constructed set of their three-dimensional phase portraits corresponding to the set of control
vectors is formulated. The definition of a stereo portrait of a three-dimensional dynamic system is intro-
duced, and a mechanism for its creation is presented; this mechanism consists in achieving some anima-
tion effect, which helps the spatial perception of images on the visual control panel. The definition of
the domain of holding states is introduced for a particular class of three-dimensional models with mul-
tiple stationary states, and algorithms for the approximation of the boundaries of these domains in the
extended space of phase variables and controls are developed. A description of the operation of a man–
machine visual monitoring system and a step-wise control designated for a wide range of state variables
are given.
Keywords: nonlinear dynamics, multiplicity of stationary states, 3D phase portrait, control visualization
DOI: 10.3103/S014641161101007X
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