Vol 77, No 8 (2016)

For a double-input single-output system, this paper defines a disturbance attenuation level (called H_∞/γ₀ norm) as the maximum-value L₂ norm of the output under an unknown disturbance with a bounded L₂ norm supplied to the first input and an impulsive disturbance in the form of the product of an unknown vector and the delta function supplied the second input, where the squared L₂ norm of the former disturbance plus the quadratic form of the impulsive disturbance vector does not exceed 1. Weight matrix choice in the H_∞/γ₀ norm yields a trade-off between the attenuation level of the L₂ disturbance and the attenuation level of the impulsive disturbance in corresponding channels. For the uncertain systems with dynamic or parametric uncertainty in the feedback loop, a robust H_∞/γ₀ norm is introduced that includes the robust H_∞ and γ₀ norms as special cases. All these characteristics or their upper bounds in the uncertain system are expressed via solutions of linear matrix inequalities. This gives a uniform approach for designing optimal and robust control laws with the H_∞/γ₀, H_∞ and γ₀ performance criteria.

This paper considers a problem of attenuation of uncertain stochastic disturbances exciting a linear discrete time-invariant system. The system’s abilities to attenuate the external disturbances are quantitatively characterized by its anisotropic norm. The anisotropic control problem is solved for a standard plant with several groups of channels from the external disturbance inputs to the controlled outputs. These channels have different levels of statistic uncertainty measured in terms of the mean anisotropy. The considered technique also allows to design the anisotropic controllers that ensure the closed-loop poles to be placed in some given convex region of the complex plain.

We consider a general approach to approximate studies of optimal control problems on the abstract level with various representations and transformations of the object model, extension principles, localizations, sufficient optimality conditions, and on the qualitative level, the search for an approximate globally optimal control. Here we use and develop transformation methods for degenerate problems that are characteristic for applications in various domains. The resulting solution can serve as an initial approximation in subsequent iterative optimization procedures whose construction methods and properties are considered in the second part of the paper.

Consideration was given to the Robbins–Monro procedure for which the Dvoretzky theorem of its convergence rate was generalized. The rate of convergence is still the most important problem of the theory of stochastic approximation.

We consider a model of a multi-server queueing system with losses caused by lack of resources necessary to service claims. A claim accepted for servicing occupies a random amount of resources of several types with given distribution functions. Random vectors that define the requirements of claims for resources are independent of the processes of customer arrivals and servicing, mutually independent, and identically distributed. Under the assumptions of a Poisson arrival process and exponential service times, we analytically find the joint distribution of the number of customers in the system and the vector of amounts of resources occupied by them. We show sample computations that illustrate an application of the model to analyzing the characteristics of a videoconferencing service in an LTE wireless network.

We consider an online adaptive forecasting algorithm for time series elements. Based on this algorithm, we define a universal strategy for the financial market: such a strategy ensures asymptotically maximal profit compared to any trading strategy where decisions are made based on rules that depend continuously on the input information. To reduce risk, in simultaneous trading of several financial instruments we perform adaptive redistribution of the current capital among them according to the AdaHedge algorithm. We propose variations of a combined game with various algorithmic trading strategies. We give results of numerical experiments based on historical data of the MICEX and BATS (US) trading platforms.

We consider the multi-fault localization problem in the observation points matrix of a discrete device. The previously proposed matrix fault localization method is extended to multiple faults. The proposed approach leads to reducing the cost of testing hardware.

This paper considers the feasibility of using the optimal parameters of stationary inventory control policies to design inventory control rules in supply systems operating on a real market. The efficiency of the long-sighted and myopic inventory control policies is compared. Different approaches to design the optimal stationary policies are investigated. A comparative evaluation of these approaches is given and the specifics of their application are discussed. The optimal parameters of the stationary inventory control policies as functions of the market state and, in particular, of the inflation rate are estimated via simulation experiments.

This paper considers a noncooperative m-player best-choice game with complete information about the quality parameters of incoming candidates. Collective decision-making is based on voting. The optimal threshold strategies and payoffs of the players are found depending on the voting threshold. The results of numerical simulation are presented.

This paper introduces α-systems of differential inclusions on a bounded time interval [t₀, ϑ] and defines α-weakly invariant sets in [t₀, ϑ] × ℝ_n, where ℝ_n is a phase space of the differential inclusions. We study the problems connected with bringing the motions (trajectories) of the differential inclusions from an α-system to a given compact set M ⊂ ℝ_n at the moment ϑ (the approach problems). The issues of extracting the solvability set W ⊂ [t₀, ϑ] × ℝⁿ in the problem of bringing the motions of an α-system to M and the issues of calculating the maximal α-weakly invariant set W^c ⊂ [t₀, ϑ] × ℝⁿ are also discussed. The notion of the quasi-Hamiltonian of an α-system (α-Hamiltonian) is proposed, which seems important for the problems of bringing the motions of the α-system to M.