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## Гарантированное управление нелинейным объектом (на примере ядерного реактора на тяжелой воде)

The task of designing the control actions for a heavy water reactor under uncertainty changes its parameters considered in the key differential game. The possibility of representing nonlinear dynamics of the object in the form of a system with parameters depending on the state (State Dependent Coefficients) and quadratic functional qualities allow you to go from having to solve a scalar partial differential equation (the Hamilton-Jacobi-Bellman) to the Riccati equation with parameters depending on the state. Feasible solution obtained by applying the min-max method. The results of mathematical modeling system in the shutdown of a nuclear reactor.

An optimal control problem is formulated for a class of nonlinear systems for which there exists a coordinate representation transforming the original system into a system with a linear main part and a nonlinear feedback. In this case the coordinate transformation significantly changes the form of original quadratic functional. The penalty matrices become dependent on the system state. The linearity of the transformed system structure and the quadratic functional make it possible to pass over from the Hamilton–Jacoby–Bellman equation (HJB) to the state dependent Riccati equation (SDRE) upon the control synthesis. Note that it is rather difficult to solve the obtained form of SDRE analytically in the general case. In this study, we construct the guaranteed control method from the point of view of the system quality based on feedback linearization of the nonlinear system; the transformation of the cost function upon linearization is examined, as well as the system behavior in the presence of disturbance and the control synthesis for this case. The presented example illustrates the application of the proposed control method for the feedback linearizable nonlinear system.

The chapter studies a dynamic risk model defined on infinite time interval, where both insurance and per-claim reinsurance policies are chosen by the insurer in order to minimize a functional of the form of variation coefficient under constraints imposed with probability one on insured's and reinsurer's risks. We show that the optimum is achieved at constant policies, the optimal reinsurance is a partial stop loss reinsurance and the optimal insurance is a combination of stop loss and deductible policies. The results are illustrated by a numerical example involving uniformly distributed claim sizes.

An optimal control problem is formulated for a class of nonlinear systems for which there exists a coordinate representation (diffeomorphism) transforming the original system into a system with a linear main part and a nonlinear feedback. In this case the coordinate transformation significantly changes the form of original quadratic functional. The penalty matrices become dependent on the system state. The linearity of the structure of the transformed system and the quadratic functional make it possible to pass over from the Hamilton–Jacoby–Bellman equation to the Riccati type equation with state-dependent parameters upon the control synthesis. Note that it is impossible to solve the obtained form of Riccati equation analytically in the general case. It is necessary to approximate the solution; this approximation is realized by numerical methods using symbolic computer packages or interpolation methods. In the latter case, it is possible to obtain the suboptimal control. The presented example illustrates the application of the proposed control method for the feedback linearizable nonlinear system.

Book include abstracts of reports presented at the IX International Conference on Optimization Methods and Applications "Optimization and applications" (OPTIMA-2018) held in Petrovac, Montenegro, October 1 - October 5, 2018.

Proceedings include extended abstracts of reports presented at the III International Conference on Optimization Methods and Applications “Optimization and application” (OPTIMA-2012) held in Costa da Caparica, Portugal, September 23—30, 2012.

The estimation of reachability sets for systems of high dimensions is a challenging issue due to its high computational complexity. For linear systems, an efficient way of calculating such estimates is to find their set-valued approximations provided by ellipsoidal calculus. The present paper deals with various aspects of such approach as applied to systems of high dimensions with unknown but bounded input disturbances. We present an innovative technique based on parallel computation that involves on-line mixing of ellipsoidal tubes found in parallel. This improves robustness of the ellipsoidal estimates. Finally discussed is an implementation of the algorithm intended for supercomputer clusters.

Quite many engineering problems, problems from ecology, medicine, and social sciences are characterized by the presence of factors bringing uncertainty into the corresponding control systems. Additional difficulties for control action construction arise in the case when the objects are described by nonlinear highorder evolutionary equations. An important subset of these objects consists of the object with interval parametric uncertainty with a given control objective and with a given a given termination time of the transient process. For this objects, one of the possible ways of control action synthesis is the application of the guaranteed control concept. We propose the method of control synthesis for one class of nonlinear uncertain objects with using their robust models having linear structure and the parameters, depending on their state.

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.