We develop a projective approach to nonlocal improvement of controlling functions and parameters in nonlinear optimal control problems for differential and discrete systems. The approach is based on getting exact (without residual terms in decompositions with respect to state and control variables) increment formulas in special differential- and discrete-algebraic conjugate systems. Examples are given.

In situations when a group of people has to make a decision based on the set of individual preferences, they use a certain aggregation method, in particular, voting. One of the main problems for any non-dictatorial social choice rule is the possibility for the voters to achieve a more preferable outcome of the voting by misrepresenting their preferences. Such actions on behalf of the voters are called manipulation, or strategic voting. One approach used to compare social choice rules in terms of how hard they are to manipulate is to find the complexity classes of manipulation problems for a given aggregation method. In this work, we present a survey of the studies of complexity classes of manipulation problems under various model assumptions and constraints.

The paper studies the problem of achieving consensus in multi-agent systems in the case where the dependency digraph Г has no spanning in-tree. We consider the regularization protocol that amounts to the addition of a dummy agent (hub) uniformly connected to the agents. The presence of such a hub guarantees the achievement of an asymptotic consensus. For the "evaporation" of the dummy agent, the strength of its influences on the other agents vanishes, which leads to the concept of latent consensus. We obtain a closed-form expression for the consensus when the connections of the hub are symmetric; in this case, the impact of the hub upon the consensus remains fixed. On the other hand, if the hub is essentially influenced by the agents, whereas its influence on them tends to zero, then the consensus is expressed by the scalar product of the vector of column means of the Laplacian eigenprojection of Г and the initial state vector of the system. Another protocol, which assumes the presence of vanishingly weak uniform background links between the agents, leads to the same latent consensus.

Active identification methods for the temporal characteristics of objects in information and control systems are reviewed. A comparative analysis of the efficiency of binary signals, i.e., pseudo-random and regular sequences of rectangular pulses in this identification problem is performed. The above analysis covers constraints imposed on the amplitude of a reference signal and on the variance of the output’s useful component. And finally, recommendations on efficient signal choice depending on the specific conditions of identification are given.

This paper solves the problem of usefull random signal filtering in a discrete-time nonlinear observation model. As such model, we consider the multiplicative model with nonnegative signals and noises. In contrast to standard filtering problems, our statement assumes that the distribution and equation of the useful signal are unknown. To solve the nonlinear filtering problem, the idea is to employ a generalized optimal filtering equation with a feature that the optimal estimator is expressed only through characteristics of the observed process. The role of such characteristics in the equation belongs to the logarithmic derivative of the conditional multidimensional density of observations. We find the solution of the equation using nonparametric kernel estimation methods with nonsymmetrical gamma kernel functions defined on the positive semiaxis. Moreover, we establish convergence conditions for the kernel estimator of the logarithmic derivative of the multidimensional density by dependent observations, as well as derive explicit formulas for optimal bandwidths and construct a stable (regularized) filtering estimator.