For secondary data processing tasks, a hybrid-robust method is developed to estimate various numerical characteristics (linear functionals) optimally under parametric uncertainty factors related to the information process, regular and irregular interferences, and the correlation function of measurement noise (including the case of nonlinear parameters). The method is fully or partially invariant with respect to these factors and yields the desired estimates without expanding the vector of estimated parameters or employing linearization procedures. A comparison with known estimation methods is presented, and the random and methodological errors, as well as the achieved computational effect, are analyzed. An illustrative example is provided.

This paper considers the problem of estimating (identifying) the magnitude of unknown inputs in engineering systems described by nonlinear dynamic models with measurement noises, which is necessary to compensate for the effect of such inputs. The solution of the problem is based on minimal-order interval observers, and their explicit relations are obtained. Such an observer and a differentiator are used to derive relations for an interval estimate of the magnitude of unknown inputs. The theoretical results are illustrated by a practical example of estimating the magnitude of unknown inputs on an electric drive of a manipulator robot. The simulations in MATLAB demonstrate the correctness of the theoretical results. The above relations can be used to design fault-tolerant systems.

This paper considers a Lagrangian system subjected to positional forces. By assumption, the frequencies of small oscillations for an equilibrium are incommensurable. The existence of multifrequency symmetric oscillations in the neighborhood of the equilibrium and their extension to global families of such oscillations is established; the families fill the entire domain of the phase space adjacent to the equilibrium. A nonlocal continuation of the above families in the system parameter is proved. In the conservative case, an autonomous control is found, and a symmetric multifrequency oscillation is stabilized in the large. In this case, feedback on potential energy is constructed.

Modern methods for mitigating nonlinear inverter voltage distortions in low-power microgrid systems are considered: proportional-resonant/multi-resonant controllers, virtual impedance and droop control, dual voltage inverters, and self-oscillating class D amplifiers. The study outlines the fundamental properties and the principle of parasitic harmonic mitigation. Special attention is paid to the number of controllers required to implement each of the methods, the effectiveness of nonlinear distortion mitigation through the study of the number of harmonics, and the reduction of the total harmonic distortion with and without the application of each method. The compatibility of each method with the output power controller is also analyzed. The benefits and drawbacks of existing methods are analyzed, as well as the prospects of using a self-oscillating class D amplifier for the control of nonlinear distortions in microgrid systems.

Questions of the organization of movement in transport networks are considered. The emphasis is placed on the most simple and cheap solutions. Optimal nodal navigation in a network with insignificant traffic jams is sought. It is proved that, for a square grid, the fastest movement to the origin of coordinates will be obtained when the route tends to the coordinate diagonals with subsequent winding on them.

A model of the COVID-19 epidemic in a population heterogeneous by chronic noncommunicable diseases is presented. A synthetic population is recreated, preserving the causal relationships between chronic diseases, sex, and age. Infection of individuals in the population is simulated, and the effect of the dependence of the course of COVID-19 on the presence and type of specific chronic diseases in infected individuals is modeled. The results of the epidemic modeling in the original population are compared with those in populations with reduced prevalence of chronic non-communicable diseases. Diseases whose reduced prevalence leads to the greatest reduction in COVID-19 mortality, the number of years of life lost, and the load on intensive care equipment are identified.

For multi-criteria decision-making problems, by analogy with qualitative probability, the concepts of complete and partial qualitative importance are introduced as binary relations satisfying certain postulated properties. A new definition of a non-strict preference relation on the set of decision alternatives, generated by qualitative importance, is proposed, and its properties are examined. Analytical rules for pairwise comparison of alternatives in terms of preference are provided. The new preference relations are compared with those developed earlier for problems in which only individual criteria are initially ordered by importance. It is shown that when all criteria are completely ordered by importance, the two preference relations coincide.

On May 6, 2026, at the age of 75, Professor Andrei Ivanovich Kibzun passed away. He was an outstanding Russian scientist in probability theory, stochastic system optimization, probabilistic methods of systems analysis, stochastic programming, and the optimization of probabilistic and quantile performance criteria. He was also a talented educator, a remarkable colleague, and a kind friend.