Том 78, № 12 (2017)

Consideration was given to a special class of the hybrid systems with switchings of time-invariant linear right-hand sides. A narrower subclass of such systems, that of connected switched linear systems, was specified among them. The necessary and sufficient frequencydomain conditions (criteria) for the existence of a common quadratic Lyapunov function providing stability of the switched systems were proposed for them. The specified subclass includes control systems with several nonstationary nonlinearities from the finite sectors that are the matter at issue of the theory of absolute stability. For the connected switched linear systems of a special kind (triangular type systems), the separate necessary and separate sufficient existence conditions were obtained for such Lyapunov functions. The interrelations between these conditions were discussed in the example.

Consideration was given to the nonlinear multiple-input multiple-output systems under the action of unmatched exogenous perturbations. For the general systems where the conditions for bounded problem of autonomous control are not met, formalized were the organization principles and existence conditions for the affine block input–output form underlying the block design of the basic law of open-plus-closed-loop control providing invariance of the output variables with respect to the exogenous perturbations. The constructions are augmented by the derivatives of the exogenous and control actions, but in distinction from the existing approaches their generating dynamic models are not included. To realize the basic law of control, used is an observer of the mixed phase and exogenous variables based on a virtual system with respect to the tracking errors with closed local links. An original decomposition procedure to design correcting observer actions was presented as a linear saturation functions estimating the mixed variables with the desired precision.

We consider the problems of developing hybrid wireless systems based on laser and radio technologies. We present a new method for estimating the characteristics of such systems operating in a random semi-Markov environment. The method is based on the theory of Markov modulated processes. We develop an efficient algorithm for computing the stationary probability distribution of the states and performance characteristics for hybrid systems. A numerical example illustrates the proposed approach.

We design a control algorithm for objects under parametric uncertainty, external bounded disturbances, and saturation of the controlled signal. We assume that the object model is described by a linear dynamical system with arbitrary relative degree and several inputs and outputs. The developed algorithm provides approximate tracking of the output of the control object for a reference signal. We obtain sufficient stability conditions for the closed system that depend on object parameters, reference model, and the controller. We show modeling results that illustrate the operation of the developed scheme.

We consider the set of control points in a discrete device where testing is organized in groups with a signature analyzer. We solve the localization problem for a fault of any multiplicity located in one or different groups. For this purpose, in addition we construct various partitions of the set of control points where we organize similar group testing. We show an algorithm for constructing additional partitions. We solve the minimization problem for the testing hardware needed to implement it.

We propose an approach to navigation for an unmanned aerial vehicle based on finding elements of motion (EM) (linear and angular velocities) by processing the field of local velocities for the motion of an image taken by an onboard video camera. The field of velocities for the image motion, the so-called optical flow (OF), is a linear function of the EM, which allows to use it to find the latter and thus provides an additional way of navigation, which can be rather efficiently used for certain specific problems solved by an UAV in autonomous flight. In this work, we use an algorithm for computing the OF for a given motion of the vehicle (direct problem) and show how to reconstruct the motion of the vehicle by OF observations with methods of statistical estimation (inverse problem).

We consider a mathematical model of borrower behavior in an annuity mortgage. The price of the apartment, amount of the borrower’s own capital, the probability distribution of his income at each time moment, and the interest rate are known. The problem is to find the loan size and schedule of payments that minimize both the total payment and the borrower’s risk. We pay the most attention to the problem of optimal reserves of capital. We study a variation of this problem where it is allowed to open an additional credit line.

This paper considers an approach to organize system diagnosis using a common control testing and 14 subsets composed of four additional checks for each “faulty” subsystem. We suggest a way to construct the subset of diagnostic checks that yields uniform check syndromes of the components with the same indexes in any faulty subsystem. We note that the required accuracy of diagnosis is guaranteed by the difference of check syndromes in any faulty subsystem. An example illustrates application of an algebraic-logical method to decode the results of checks.

We suggest an algorithm to optimize reliability of an electric power system. The algorithm uses the averaged dual estimates of power generation and power flow constraints. The average values of dual estimates are found by analyzing electric power system reliability. The developed algorithm is based on the enumeration of alternative system reconfiguration scenarios, while the study of average dual estimates allows to reduce the number of scenarios considered. Finally, we present the results of numeric simulations.

This paper proposes a strengthening of the author’s core-accessibility theorem for balanced TU-cooperative games. The obtained strengthening relaxes the influence of the nontransitivity of classical domination αv on the quality of the sequential improvement of dominated imputations in a game v. More specifically, we establish the k-accessibility of the core C(α_v) of any balanced TU-cooperative game v for all natural numbers k: for each dominated imputation x, there exists a converging sequence of imputations x₀, x₁,..., such that x₀ = x, lim x_r ∈ C(α_v) and x_r−m is dominated by any successive imputation x_r with m ∈ [1, k] and r ≥ m. For showing that the TU-property is essential to provide the k-accessibility of the core, we give an example of an NTU-cooperative game G with a ”black hole” representing a nonempty closed subset B ⊆ G(N) of dominated imputations that contains all the α_G-monotonic sequential improvement trajectories originating at any point x ∈ B.