Volume 77, Nº 10 (2016)

Control of network systems, or network control, is a rapidly developing field of modern automated control theory. Network control is characterized by a combination of the classical control theory toolbox (linear systems, nonlinear control, robust control and so on) and conceptually new mathematical ideas that come primarily from graph theory. Methods of network control let one solve analysis and synthesis problems for complex systems that arise in physics, biology, economics, sociology, and engineering sciences. In this survey, we present the main fields of application for modern theory of network control and formulate its key results obtained over the last decade.

A computationally efficient method for the design of a suboptimal anisotropic controller for discrete descriptor systems based on convex optimization methods is proposed. Numerical examples are given.

The optimality criteria used in the problem of stochastic linear regulator over an infinite time horizon were analyzed. A certain criterion for long-run average and pathwise ergodic were shown to be inefficient with regard for the disturbance factor. Consideration was given to a new criterion of the extended long-run average and its use in the discounted control systems.

Consideration was given to the new classes of continuous and discrete uncertain systems where the elements of the control plant matrix represent physically realizable arbitrary functionals with only the boundaries of their variation known. The stabilizing controls robust in the elements of the control plant matrix were constructed using special quadratic Lyapunov functions.

A modification of the decoding q-ary Sum Product Algorithm (q-SPA) was proposed for the nonbinary codes with small check density based on the permutation matrices. The algorithm described has a vector realization and operates over the vectors defined on the field GF(q), rather than over individual symbols. Under certain code parameters, this approach enables significant speedup of modeling.

This paper formulates and solves the mob excitation control problem in the discretetime setting by introducing an appropriate number of “provokers” at each step of control.

The mathematical model of electric circuits with diode current converters is a system with diode nonlinearity represented as a system of ordinary differential equations with a discontinuous right-hand side that has a special form. In this work, we construct and study a similar system with continuous right-hand side and large parameter K; we prove a theorem that states that solutions of the corresponding initial problems of order

\(1/\sqrt K \)

This paper proposes an algorithm generating a set of conflict-free safe trajectories in terrain conditions from an arbitrary initial position to a given synchronization point with a reference aircraft in front. We also design a speed calculation algorithm along the generated flight trajectories that ensures a required longitudinal separation margin at the synchronization point.

The optimal portfolio problem of effect-interdependent investment projects is considered. An algorithm yielding the optimal solution based on the method of network programming is suggested. The performance of this algorithm is illustrated using an example.

In the paper, two-stage network games are studied. At the first stage of the game, the players form a network, while at the second stage they choose strategies according to the network realized at the first stage. Both noncooperative and cooperative settings are considered. In the noncooperative case, the Nash equilibrium is used as a solution concept, whereas the cooperative setting involves an allocation (the Shapley value) as a solution concept. It is demonstrated that the Shapley value does not satisfy the time consistency property.