We consider a Gaussian linear-quadratic control problem with incomplete data for a stochastic object (target) from a moving observer with nonlinear dynamics in continuous time. Characteristic features of this formulation include the fact that the stochastic dynamics equation of the observation object and the actual observation equations depend on the vector of the current state of the observer. The observer’s control objective is to choose a rational trajectory of its movement in the sense of minimizing the expectation of a certain payoff functional (cost). In problems of this kind, optimal control over observations (in the considered case, control over the trajectory of the observer) is usually sought in the class of program controls, i.e., as a function of time and initial conditions. A natural question arises: what will change if we extend the class of program controls by the observer to the class of positional ones, i.e., to the class of controls that depend not only on time and initial conditions but also on the realizations of observations and the trajectory of the observer at a given time moment. We consider two meaningful special cases of the general formulation of the problem where such an extension does not improve the control quality. We give examples and proof of the theorem

The problem is investigated of optimal control of a system, described with the model of fractional-order double integrator, in which the initial and final conditions depend on the appropriate time-point selection. Several cases are considered, physically similar to the system transfer from a state of the rest to a state of the uniform linear motion, to a uniformly accelerated and to a periodic motion, and from a uniform to a uniformly accelerated motion. The dependencies are analyzed of the control norm from the control time and from the fractional differentiation index value.

The modified (due to ergodic hypothesis using) Poincare transversal cutting surface method is proposed for studying control effectiveness from data of a "passive" experiment. The obtained .quasi-recurrence-plots map makes it possible to identify lagging and successfully developing regions according to achieved level of the density of the population and level of human development.

We consider the problem of estimating the accuracy of quantitative similarity coefficients. For this purpose, we introduce a new concept of the similarity measure for the corresponding coefficient. We show that only frequency forms of quantitative similarity coefficients represent consistent estimates of their similarity measures. We obtain asymptotic confidence intervals for the Ruˇziˇcka and Bray–Curtis similarity measures based on the coefficients with the same names. We also propose a criterion for the homogeneity of two populations based on the above-mentioned coefficients.

Early detection of the threat of a cascading failure is encouraged to use the immune information system, the main subsystem of the which is a virtual stability analyzer. We propose to implement the virtual analyzer by usage of the linearized models of energy systems and apparatus Lyapunov direct method, based on the study of matrix Lyapunov equation solutions, called gramians. The functional of stability loss risk is defined as the square of H 2 - norm of the system matrix transfer function, which is proportional to the energy of the system. We propose to use the functional of a risk assessment through the spectral decomposition of energy participation factors for the evaluating of the energy accumulated in dominant eigenvalues of the system. For sub-gramians method the energy participation factors are defined as a partion derivative of the functional regarding to the chosen parameter. In comparison with the method of a modal analysis the proposed approach allows to evaluate the impact of synergies between weak-stable eigenvalues and their combinations to the system stability loss risk, and also to detect the potential source of stability loss.