Ivan N. Barabanov

Dynamic models of informational control in social networks

The dynamic models of informational control in social networks were considered. The problems of analysis and design of the optimal controls were posed and examined.

Basic oscillation mode in the coupled-subsystems model

Consideration was given to the model obeying a system of ordinary differential equations where the subsystems are systems of autonomous ordinary differential equations. If the coupling parameter ɛ = 0, then the model falls apart into decoupled subsystems. For a model consisting of coupled subsystems, considered was the main mode for which the problems of oscillations, bifurcation, and stability were solved, and the results obtained before for the case of two second-order subsystems were generalized.

Oscillation family in weakly coupled identical systems

Consideration was given to an autonomous model with weakly coupled identical subsystems. Existence of a family of periodic solutions which is similar to the family in a subsystem was established. A scenario of bifurcations of the characteristic exponents was given, and the stabilization problem was solved. An example was given.

Stabilization of oscillations from a monoparametric family of the autonomous system

The problem of oscillation stabilization is solved for the autonomous system in the case when the oscillations form a monoparametric family. For each possible point type of the family the explicit formulae that solve the problem are obtained. It follows from those formulae that the dissipation is a necessary condition of the stabilization. The obtained sufficient conditions of the stabilizations coinside with the appropriate necessary conditions to within the sign of unstrict inequality.

On the Model Containing Coupled Subsystems

The model containing coupled subsystems (MCCS), which decouples into indepen- dent subsystems as the coupling vanishes, is considered. The subsystems of the MCCS are described by autonomous systems of ordinary differential equations. Each subsystem is sup- posed to admit a single parameter family of periodic motions. The general characteristics of the MCCS are presented. Some problems concerning the MCCS are stated, i.e. the problems of oscillations existence, bifurcations, stability, stabilization, and resonance. The classification of MCCS is proposed, the currently investigated classes of MCCS are announced. One class of MCCS is studied in detail, the corresponding results are presented. In this paper we study the model containing coupled subsystems. This model is described by a system of ordinary differential equations (ODE), where subsystems are autonomous ODEs. The coupling is characterized by a numeric parameter e, which can be either scalar or vector. The subsystems become independent as e = 0. If e is vector then the MCCS can be of hierarchical structure, where subsystems are coupled on various levels. In the general case subsystems are either linear or nonlinear, of arbitrary order, and of various nature. The N-planet problem serves as an example of the MCCS with single-leveled subsystems. The following are some more examples of the MCCS: multi-link pendulum, chain of spring oscillators, Sun-planets-satellites system (a system of two levels), translationally and rota- tionally moving space vehicles, in particular, artificial Earth satellites, robot systems with cross-coupling, model of DNA oscillations, coupled neurons, wind turbine (electromechan- ical system), mechatronic systems, etc.

Designing a stable cycle in weakly coupled identical systems

Consideration was given to a dynamic model containing weakly coupled identical subsystems. The subsystem was assumed to admit a family of periodic solutions where the period is a monotonic function of one parameter. Requirements on the coupling under which the model has an asymptotic orbital stable cycle were established. The problem of stabilization of the model oscillations by a small smooth autonomous coupling control was solved using the results obtained. The system of two coupled conservative systems with one degree of freedom was considered individually.

An orbitally asymptotically stable cycle in weakly coupled identical systems

The dynamical model containing coupled identical subsystems is considered. A subsystem is supposed to admit of a family of periodic solutions with the period being a monotonic function of a single numerical parameter. Conditions to be imposed on couplings such that the whole system admits a family Σ of periodic motions similar to that of a subsystem are found. An orbitally asymptotically stable cycle is distinguished in Σ.

Oscillations of weakly coupled identical systems

The problem of existence of isolated periodic solutions in the model containing coupled subsystems (MCCS) is considered. Systems are coupled by weak connections and become independent as connections vanish. The basic oscillations mode is considered. Connections are assumed to be either time-independent, or time-periodic.

Quasiautonomous system: Oscillations, stability, and stabilization at the ordinary point of the family of periodic solutions

Consideration was given to the single-frequency oscillations of the periodic system allied to the nonlinear multidimensional autonomous system. It was assumed that the generating autonomous system admits a family of solutions with period depending on a single parameter: all points of the family break down into the ordinary points whose derivative of the period with respect to the parameter is other than zero and the critical points where this derivative vanishes. Generation of oscillations and their stability at the ordinary point of the family were studied. These problems were solved earlier for the second-order system.

Dynamic models of mob excitation control in discrete time

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.