Vol 80, No 3 (2019)

The optimal speed problem for the class of linear discrete-time systems with the infinite-dimensional state vector and degenerate operator is solved. Some properties of convex sets are formulated and proved. Necessary and sufficient conditions under which this problem has a solution in the case of the zero point located on the boundary of the reachability set are established. The optimality conditions are written as a discrete-time maximum principle. For the inner points, the degenerate character of the maximum principle is demonstrated. For an inner point, the optimal speed problem is solved by developing an algorithm with reduction to the admissible case of the boundary point. Some examples are given.

This paper considers the stability of singular switched systems with homogeneous functions in the right-hand sides of the corresponding equations. Stability conditions of the complete system with an arbitrary switching mode are established through its decomposition into the isolated subsystems of fast and slow motions. A stabilizing feedback control design method based on measurements of the fast variables only is suggested.

We propose a method of supervised estimation with a training set of the posterior probabilities of an object belonging to classes according to a collection of known values of its features. These probabilities represent comprehensive information for solving the classification problem. They allow to solve the classification problem under various criteria (maximum probability, minimum average cost of error, etc.), which are usually chosen subjectively. Our approach to solving this problem is based on the construction of a series of approximations of special discriminant functions at whose zero points the posterior probabilities of the classes are specified during their construction. The heuristic approximation algorithm of the discriminant function used in the neighborhood of zero values is a part of the method. In the method, there is no need for additional modifications such as the Platt’s calibrator for the method of support vector machines. We give model examples of applying the proposed approach and an example from medical diagnostics with real data.

For a symmetric unimodal random variable with known mode and variance, we construct a tight upper bound for the probability of falling outside an arbitrarily specified interval. We define the distribution on which the bound is achieved. In the special case when the distance between mode and the middle of the interval is less than 29% of its radius, the resulting bound is determined by the Gauss inequality. We have applied our result to the construction of robust confidence intervals.

We propose a method of simplified group target assignment, not only providing the assignment of targets to interceptors but also making it possible to construct expected intercept trajectories taking into account real-world restrictions, elimination of participants, and target priorities.

The problem of binary classification is considered, an algorithm for its solution is proposed, based on the method of entropy-based estimation of the decision rule parameters. A detailed description of the entropy-based estimation method and the classification algorithm is given, the advantages and disadvantages of this approach are described, the results of numerical experiments and comparisons with the traditional support vector machine for classification accuracy and degree of dependence on the training sample size are presented.

Usually in the context of the anisotropy-based robust performance analysis stochastic systems with zero initial condition are investigated. In this paper we extend this analysis and consider a linear discrete time invariant system under random disturbances and with the nonzero initial condition. In accordance with the basic postulates of the anisotropy-based control theory the disturbance attenuation capabilities of system are quantified by the anisotropic generalized gain which is defined as the largest root mean square gain of the system with respect to a random input and the nonzero initial condition, anisotropy of which is bounded by a given nonnegative parameter a.

This paper considers a network game as follows. In each node of a network, economy is described by the simple two-period Romer’s model of endogenous growth with production and knowledge externalities. The sum of knowledge levels in the neighbor nodes causes an externality in the production of each network node. The concept of node type is introduced and a corresponding typology of networks is suggested. As demonstrated below, all inner equilibria of the game are determined by this typology. For several typologies, the equilibrium knowledge levels are found in explicit form for the nodes that have different positions in the network.

The paper presents an algorithm for nondestructive inspection of the number of threads in webs during their formation. It describes ASK-Tkachestvo information and control system enabling the automation of web quality monitoring based on the algorithm proposed.