A gyrostat in central Newtonian gravitational and dipolar magnetic fields is considered. It moves along a weakly elliptical Keplerian orbit in a magnetic equatorial plane. The gyrostat possesses electrostatic charge and intrinsic magnetic moment. The attitude motion under the action of Lorentz and magnetic torques is studied. It is shown that the system of differential equations of gyrostat attitude motion is reversible with three fixed sets in the case of a circular orbit. Symmetrical periodic motions of oscillatory type are analyzed. Bifurcation in a family of gyrostat symmetrical oscillations and generation of two isolated symmetrical oscillations are revealed in transition from a circular orbit to an elliptical one.

For a locally stable polynomial dynamical system its region of attraction can be estimated by a polynomial Lyapunov function level set. We formulate this problem in terms of global minimization of a polynomial function over single polynomial constraint. We describe a simple Matlab tool, which employs numerical algebraic geometry methods for computing all local solutions of the optimization problem and therefore its global solution.

The paper presents an approach to the statistical linearization of the input/output mapping of non-linear discrete-time stochastic systems driven by a white-noise Gaussian process. The approach is based on applying the quadratic mutual Rényi information. Within such an approach, the statistical linearization criterion is the condition of coincidence of the mathematical expectations of the output processes of the system under study and the derived model and the condition of coincidence of the quadratic mutual Rényi information of the input and output processes of the system and the quadratic mutual Rényi entropy of the input and output processes of the model. As a result, explicit analytical expressions to derive coefficients of the weight function of the target linearized model are obtained. The consideration is preceded with an analysis of applying consistent measures of dependence within the system identification.

In this paper we consider a special problem of formation control, that is, the problem of uniform spread (or deployment) of several identical agents on a line segment. This problem was exhaustively studied for first-order agents since the pioneering paper by I.A. Wagner and A.M. Bruckstein who considered it under the name of ``row straightening algorithm''. We extend it to the more realistic case of second-order agents.

During the last decade, automated process control systems (APCS) have approached a qualitatively new level of the development; and a consequence of this progress is considerable complicating the APCS software and its life cycle. In 2000, at the V.A. Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences (ICS RAS), software complexes for perspective nuclear power plant (NPP) APCS has been elaborated The required life cycle of the total APCS is not less than 30 years, what leads to a necessity of developing and implementing comprehensive procedures on maintaining and modification of the software complexes. In the paper, an experience gathered in the ICS RAS on maintaining NPP APCS software, assuring quality of the updated software code and forecasting of costs of its modification and maintenance is presented.