This paper considers a time-invariant system with a set of imperfect measurements, the useful component of which may be unavailable at certain times. Virtual objects duplicating the state of the original object are introduced, and an output estimate is constructed for each of them. Using vectorization, an extended model of the system is derived in the form of a linear discrete time-invariant system with multiplicative noises. The external disturbance is chosen from the class of sequences of random vectors with a bounded level of mean anisotropy. For the system describing the estimation error dynamics, conditions for the boundedness of the anisotropic norm are obtained, under which the chosen type of estimator exists. An invertible linearizing change of variables is indicated, which allows reducing the problem of finding the estimator matrices to checking the solvability of a special system of linear matrix inequalities with a convex constraint.

This paper is devoted to the kinematic problem of the optimal, in terms of energy consumption, program angular acceleration of a spacecraft under arbitrary boundary conditions imposed on its angular position and angular velocity. A quasi-optimal analytical solution of the problem is obtained within the classical Poinsot concept of the angular motion of a solid body as a generalized coning motion and Pontryagin’s maximum principle. This solution is brought to an algorithm. Supporting analytical and numerical examples are provided to show either the proximity of the quasi-optimal and optimal solutions or their complete coincidence, depending on the boundary conditions.

This paper presents a time-varying control law designed for an interceptor’s guidance to an intensively maneuvering aircraft (aerial target). The control law takes into account the mismatch between the dynamic properties of the interceptor and the target. Simulation results are provided, indicating the potential feasibility of intercepting the target and improving guidance accuracy.

In the presented paper, a one-stage problem of simultaneous finding an optimal insurance and investment portfolio in the presence of background risks is studied. The goal functional is a functional of Markovitz type which depends on the first two moments of the final capital. It is shown that the optimal insurance necessarily belongs to a class of stop loss insurances, equations determining parameters of the stop loss insurance and investment portfolio are derived. A numerical example illustrating the theoretical results is given.

Forecasting critical transitions in epidemic incidence is important for epidemic surveillance. Earlier detection can support a more timely public-health response. This paper studies anomaly detection methods based on artificial intelligence and early warning signals (EWSs) in incidence time series. The goal is to predict transitions from seasonal infections to epidemic outbreaks. Two approaches are examined. The first is a classification approach that estimates whether a critical transition is near. The second is a regression approach that forecasts future infection dynamics. Several machine learning models are applied to two types of data. The models include ensemble methods (Easy Ensemble, RUSBoost, and Balanced Bagging) and deep learning architectures (Early Warning Signal Network (EWSNet), LSTM, and GRU). The first dataset contains influenza incidence with epidemic periods labeled by expert criteria. The second dataset contains unlabeled COVID-19 incidence. The results show that Easy Ensemble and EWSNet provide the best balance between precision and recall. Recurrent neural networks model the dynamics of mean values effectively, whereas variance forecasting remains more difficult. The results show that classical EWS methods and machine learning can be combined to improve epidemic forecasting and support public-health decision making.

Numerous studies are devoted to systems of connected agents and network control. Historically, the greatest interest of control theory has been in averaging systems, particularly the consensus problem. However, network interaction can be characterized by more specific functions reflecting the dependence on the actions of network neighbors, which is particularly evident in models of strategic interaction on a network, the subject of game theory. This paper surveys game-theoretic models of network interaction from the class of linear best-response games. The models are formally described, and formulations of control problems in this class of games are considered. Special attention is paid to the connection with consensus models and the well-known related control problems that can be stated in terms of a strategic interaction of agents. Despite the general similarity with the models of linear systems from control theory, this class of games allows capturing qualitative aspects of strategic interaction of connected agents and highlighting the role of structural characteristics.