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## Метод расширенной линеаризации в задаче управления неопределенным нелинейным объектом.

In this paper, using the theory of differential games developed the algorithm of constructing guaranteed control for nonlinear systems. Through the transition from the nonlinear model to model the linear form with parameters that depend on the state, will move from finding solutions to equations of Hamilton-Jacobi-Bellman equation to the Riccati equation. Moreover, the appointment of the "worst settings" will make the matrix not depend on the state that will allow you to solve Riccati equation and to synthesize the required control. The example of construction controls for non-linear mathematical model of the human immune system in the presence of the HIV. Built management controls the supply of antiretroviral drugs to maintain healthy cells of the human immune system at the required level to maximize and facilitate the life of the patient.

Mathematical models of nonlinear systems of a certain class allow them represented as linear systems with nonlinear state feedback. In other words, let make the appropriate coordinate transformation of the original dynamic model. Such a transformation, using Lyapunov functions, a number of studies used to determine the parameters of regulators to ensure the asymptotic stability properties of the nonlinear system, ie guaranteeing bounded trajectories emanating from the initial states of the system. For linear systems, there is a powerful and convenient mathematical apparatus allows the synthesis of optimal controls, but this unit is not applicable or partially applicable for nonlinear systems. Unlike prior work in this paper for nonlinear systems linearizable feedback as in the synthesis of optimal control problems with quadratic performance applied the method based on the use of the Riccati equation with parameters depending on the state.

This book is devoted to game theory and its applications to environmental problems, economics, and management. It collects contributions originating from the 12th International Conference on “Game Theory and Management” 2018 (GTM2018) held at Saint Petersburg State University, Russia, from 27 to 29 June 2018.

This volume is dedicated to the 80th anniversary of academician V. M. Matrosov. The book contains reviews and original articles, which address the issues of development of the method of vector Lyapunov functions, questions of stability and stabilization control in mechanical systems, stability in differential games, the study of systems with multirate time and other. Articles prepared specially for this edition.

The influence of different forms of housing cryobot speed and efficiency of movement them into the ice structures. The problems of cryobot to study the ice surface in Europe

We discuss the materials associated with the formation of chaotic bands on the ice surface on Europe, a satellite of Jupiter. There are suggestions as to their origin.

Nowadays, production control problems has been widely studied and a lot of valuable approaches have been implemented. Some work addresses the problem of tracking the uncertain demand in case of uncertain production speeds. The uncertainties are described by deterministic inequalities and the performance is analyzed in from of the worst-case scenario. First, simple mathematical models are introduced and the control problem is formulated. In continuous-time, the cumulative output of a manufacturing machine is the integral of the production speed over time. At the same time, the production speed is bounded from below and above, and hence the manufacturing process can be modeled as an integrator with saturated input. Since the cumulative demand (which is the reference signal to track) is a growing function of time, it is natural to consider control policies that involve integration of the mismatch between the current output and current demand. In the simplest consideration it results in models similar to a double integrator closed by saturated linear feedback with an extra input that models disturbances of a different nature. This model is analyzed and particular attention is devoted to the integrator windup phenomenon: lack of global stability of the system solutions that correspond to the same input signal.

We construct an example of blow-up in a ”ow of min-plus linear operators arising as solution operators for a Hamilton…Jacobi equation @S/@t+|∇S|/ + U(x, t) = 0, where > 1 and the potential U(x, t) is uniformly bounded together with its gradient. The construction is based on the fact that, for a suitable potential de“ned on a time interval of length T, the absolute value of velocity for a Lagrangian minimizer can be as large as O(log T)2−2/. We also show that this growth estimate cannot be surpassed. Implications of this example for existence of global generalized solutions to randomly forced Hamilton…Jacobi or Burgers equations are discussed.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

The geographic information system (GIS) is based on the first and only Russian Imperial Census of 1897 and the First All-Union Census of the Soviet Union of 1926. The GIS features vector data (shapefiles) of allprovinces of the two states. For the 1897 census, there is information about linguistic, religious, and social estate groups. The part based on the 1926 census features nationality. Both shapefiles include information on gender, rural and urban population. The GIS allows for producing any necessary maps for individual studies of the period which require the administrative boundaries and demographic information.

Existing approaches suggest that IT strategy should be a reflection of business strategy. However, actually organisations do not often follow business strategy even if it is formally declared. In these conditions, IT strategy can be viewed not as a plan, but as an organisational shared view on the role of information systems. This approach generally reflects only a top-down perspective of IT strategy. So, it can be supplemented by a strategic behaviour pattern (i.e., more or less standard response to a changes that is formed as result of previous experience) to implement bottom-up approach. Two components that can help to establish effective reaction regarding new initiatives in IT are proposed here: model of IT-related decision making, and efficiency measurement metric to estimate maturity of business processes and appropriate IT. Usage of proposed tools is demonstrated in practical cases.