卷 78, 编号 4 (2017)

Nonlinear single-input affine systems represented in a canonical (normal) form are considered. The control resource is assumed to be constrained. For a closed-loop system obtained by applying a linearizing feedback, the problem of finding an estimate of the attraction domain is set. A method for constructing an ellipsoidal estimate that is based on results of absolute stability theory is suggested. Construction of the estimate reduces to solving a system of linear matrix inequalities. The discussion is illustrated by numerical examples.

For an object whose dynamics obeys a system of ordinary differential equations, application of the methods of subdifferential and hypodifferential descent to the problem of program control of object dynamics was illustrated.

We propose new sufficient conditions for saddle-node bifurcations in one- and twoparametric dynamical systems obtained with the parameter functionalization method, derive asymptotic formulas for the resulting solutions, and analyze their stability. As an application, we consider the synchronization problem for periodic oscillations of an autonomous Van der Pol generator under an external harmonic influence.

The anisotropic norm of the linear discrete time invariant system is the measure of the system output sensitivity to a random input with the mean anisotropy bounded by some nonnegative value a. The mean anisotropy characterizes the degree of predictability of the stochastic signal. The anisotropic norm of a system is the induced norm with the extreme cases of H₂ norm and H_∞ norm, respectively, under a → 0 and a → ∞. The lower bound of the anisotropic norm of the linear discrete time invariant system was established in the present paper using the methods of linear algebra.

We show the results of solving the problem of constructing an adaptive control system with nonlinear reference model for a nonstationary dynamical object with a nonlinear actuator. To analyze the dynamical properties of a nonlinear nonstationary control system we use the method of pointwise transformations. We show the results of analysis and mathematical modeling of the considered control system with the adaptation circuit switched off.

We consider methods for solving routing problems with precedence constraints that use iterative modes based on Bellman insertions while recomputing precedence constraints of the original problem; we assume that the dimension of the latter is sufficiently large, which does not let us, due to complexity of computations, immediately apply dynamic programming in the “global” version.

We consider synthesis problems for a discrete event model in a real time distributed computational system. The model reflects information exchange events between software units of the system and is intended to construct special test sequences that detect faults in these exchanges. We propose a version of the model that allows for a reduction in the relative volume of diagnostic information transmitted to diagnostic tools.

We consider the possibility to explain manifestations of collective intelligence via the presence of structure in the set of tasks may being fulfilled. A distributed system corresponds to a lattice of tasks that the system can fulfill. On this lattice, we define an external multiplication operation for lattice elements and respective operations of linear logic. The implication operation is used to choose the version of system reconfiguration, i.e., choose an executor for a new task. We show that this choice is to a large extent defined by the structure of the lattice of tasks and the definition of the multiplication operation on it. The proposed reconfiguration method is applied to an example of operation for a group of janitor robots.

We consider synthesis and modeling of hierarchical robust magnetic control systems for plasma in tokamaks with adaptation of the magnetic axis’ vertical position. The studies were done for ITER (Cadarache, France) and Globus-M (St. Petersburg, Russia) tokamaks. Our original synthesis method ensures an improvement in performance for the shape of the plasma by resolving the contradiction between position and plasma shape via adaptation in a hierarchical system. Numerical modeling of synthesized control systems on multivariable linear models of plasma and nonlinear plasma-physics code DINA that unites basic equations of plasma dynamics in a magnetic field has shown the efficiency of the proposed approach and a possibility to apply it in a physical experiment.

This paper presents a formalization and the results of solution for the problem of moving object evasion from detection on a plane. Detection is performed by a system of heterogenous stationary observers by the last transmitted signals of the primary and reflected (secondary) fields in the passive and active modes, respectively. Simulation results are given.

Approach to the solution of a problem of structural and parametrical identification of models of the soft sensors (SS) of technological plants on the basis of robust regression and information criteria is proposed. The robust regression is used for model parameter estimation, and choosing the best model structure in the sense of information criteria. SS is developed by means of the proposed approach which was tested in control systems for optimization of the process operation of gas separation section of fluid catalytic cracking unit of “OJSC Gazpromneft-Omsk Refinery.”

In this paper we consider the NP-hard 1|r_j|ΣT_j scheduling problem, suggesting a polynomial algorithm to find its approximate solution with the guaranteed absolute error. The algorithm employs a metric introduced in the parameter space. In addition, we study the possible application of such an approach to other scheduling problems.

In this paper, the estimation of a nonlinear stochastic dependence between signals in information-measuring and control systems is considered. The maximum correlation coefficient and corresponding optimal transformations of the signals are estimated using the Bernstein approximation. Some basic concepts of the copula theory are discussed. Main calculation formulas for the maximum correlation coefficient in the case of a degenerate stochastic kernel are presented. An estimation algorithm for the maximum correlation coefficient and corresponding optimal (nonlinear) transformations of random signals is proposed. An example of correlation estimation for random signals is given.

We consider a game between a group of n pursuers and one evader moving with the same maximum velocity along the 1-skeleton graph of a regular polyhedron. The goal of the paper is finding, for each regular polyhedron M, a number N(M) with the following properties: if n ≥ N(M), the group of pursuers wins, while if n < N(M), the evader wins. Part I of the paper is devoted to the case of polyhedra in ℝ³; Part II will be devoted to the case of ℝ^d, d ≥ 5; and Part III, to the case of ℝ⁴.