Tatiana Zarodnyuk - Academia.edu (original) (raw)

Papers by Tatiana Zarodnyuk

Springer proceedings in mathematics & statistics, Dec 31, 2022

Springer proceedings in mathematics & statistics, 2018

Some nonlinear and discrete optimal control problems with phase constraints on a fixed but suffic... more Some nonlinear and discrete optimal control problems with phase constraints on a fixed but sufficiently large time interval are considered as singularly perturbed problems. In continuous-time case the state equations are reduced to singularly perturbed equations on a finite time interval and, in discrete-time case, the state equations have the form of systems with a small step. Using the technique for singularly perturbed systems, the formal asymptotic expansions by the corresponding small parameter are constructed which contain the structural information about the solution. That is usually sufficient for most applications to obtain an initial approximation to control in the global optimum neighborhood. The obtained algorithms can be applied to mathematical economics and technical objects control problems with phase and control constraints, and with turnpike effects in the trajectories, where the turnpike trajectories can be discontinuous. The use of traditional algorithms for these problems is inefficient due to the large increase of computational difficulty.

2021 International Conference on Electrical, Computer and Energy Technologies (ICECET), Dec 9, 2021

The paper deals with techniques of constructing optimal control problems and testing optimization... more The paper deals with techniques of constructing optimal control problems and testing optimization software for controlled dynamical systems. A test collection of nonconvex optimal control problems has been developed and used for studying the properties of optimization software. The description of the collection problems is made using the generated template, which includes the formulation of the problem statement, characteristics of the computational process and the obtained results, containing graphical visualizations of the reachable set and optimal controls with corresponding trajectories. Several testing techniques based on presented collection are proposed.

The paper proposes a methodological approach to the construction of modern software systems, as w... more The paper proposes a methodological approach to the construction of modern software systems, as well as the creation of computing resources available via the Internet. The presented approach has been tested in practice. In the article it is considered on the example of the implementation of the integrated software INTEC for the study of the problem of energy security. Proven methods and technologies are also used to solve the problem of legacy software OPTCON for optimal control problems, which was also used to solve applied problems from various scientific and technical fields.

Optimization Letters, Dec 12, 2018

In this paper we propose an algorithm of obtaining reachable points that uniformly fill the volum... more In this paper we propose an algorithm of obtaining reachable points that uniformly fill the volume of the reachable set, and thus, result in a point cloud uniformly approximating a set even with a small number of points. To solve the task of finding each additional point is to solve the maximin optimal control problem. The design of the method allows considering reachable sets not only of two-dimensional systems but of multidimensional ones as well. The computational experiments conducted with the use of the proposed algorithm confirm the efficiency of the approach.

Ekologiya Cheloveka / Human Ecology, 2010

Важная роль в оценке и прогнозировании состояния единой медико-экологической системы отводится со... more Важная роль в оценке и прогнозировании состояния единой медико-экологической системы отводится созданию и анализу математических моделей, описывающих динамику взаимодействия элементов системы. Математические модели служат инструментом, позволяющим увязывать и согласовывать информацию различного содержания, что неизбежно в любых комплексных междисциплинарных исследованиях [3, 11]. Кроме того, с точки зрения доказательной медицины использование математико-статистических и эпидемиологических подходов абсолютно необходимо [5, 8]. В последние годы при моделировании сложных процессов и систем стали применяться нейросетевые методы, в основе которых лежит идея построения вычислительного устройства из большого числа параллельно работающих простых элементов (формальных нейронов), которые функ-ционируют независимо друг от друга и связаны между собой каналами передачи информации [2, 7]. Каждый отдельный нейрон моделируется простой функцией (обычно логистической), но совокупная высокая сложность модели, гибкость ее функционирования и другие важнейшие качества определяются структурой связей и многоуровневой иерархией всей сети. Нейронная сеть, получающая на входе определенный сигнал, способна после прохождения его по сети выдавать на выходе определен-ный ответ, который зависит от весовых коэффициентов всех нейронов, определяемых в процессе самообучения сети [13]. Цель исследования – оценить возможность использования искус-ственных нейронных сетей при изучении особенностей формирования заболеваемости населения крупного промышленного центра. В ходе работы последовательно решались следующие задачи:• разработка математической модели, учитывающей в качестве объясня-ющих переменных факторы окружающей природной и социальной среды;• определение фоновых уровней заболеваемости населения на основе нейромодели по наиболее значимым факторам внешней среды;• разработка оптимальных уровней загрязнения атмосферного воздуха, позволяющего обеспечить фоновый уровень заболеваемости различных возрастных групп населения);• проверка адекватности модели при сравнении результатов чис-ленных экспериментов.Материалы и методы исследования Исследования проведены в г. Братске, расположенном на севере Иркутской области В 1994 году по результатам государственной эколо-

The paper proposes a technology for a global extremum search, which makes it possible to estimate... more The paper proposes a technology for a global extremum search, which makes it possible to estimate the probability of finding a solution in the optimal control problems. The idea of multistart based on proposed technique enables to create the computing technology which is not strongly depend on problem dimension and oriented to finding additional information about investigated object. The paper presents solutions of two nonconvex optimal control problems for power systems.

Automation and Remote Control, Oct 1, 2022

Journal of Global Optimization, Sep 13, 2019

The paper proposes a method for finding the minimum value of a functional in nonlinear nonconvex ... more The paper proposes a method for finding the minimum value of a functional in nonlinear nonconvex optimal control problems. The method takes advantage of the hidden convexity property of the controlled differential equations systems. Application of the multistart idea with extrema selection procedures makes it possible to create software that does not strongly depend on the problem size and supplies additional information about the object under investigation. Three test problems are considered to show specific properties of using the stochastic multistart algorithm and extension numerical technology.

IOP conference series, Dec 17, 2018

Incidence prediction models for urban population have not yielded consistent or highly accurate r... more Incidence prediction models for urban population have not yielded consistent or highly accurate results. The complex nature of the interrelationship between "environmental factors and incidence" has many nonlinear associations with outcomes. We explore artificial neural networks (ANNs) to predict the complex interactions between the risk factors of incidence among the urban population. ANN modeling using a standard feed-forward, back-propagation neural network with three layers (i.e., an input layer, a hidden layer, and an output layer) is used to predict the incidences of diseases of children and adults. A receiver-operating characteristic (ROC) analysis is used to assess the model accuracy. We develop a mathematical model taking into account factors of natural, anthropogenic, and social environments. The model effectiveness is proved by computing experiments for the Bratsk industrial centre (Irkutsk region, Russia). Optimal air pollution levels are offered to achieve a background morbidity level among different age groups of the population. The prediction of incidence is most accurate when using the ANN model with several univariate influences on the outcome. An incorporation of some computerized learning systems might improve decision making and outcome prediction.

Journal of Global Optimization, Aug 5, 2015

A numerical method of a two-dimensional non-linear controllable system reachable set boundary app... more A numerical method of a two-dimensional non-linear controllable system reachable set boundary approximation is considered. In order to approximate the boundary right piecewise linear closed contours are used: a set of broken lines on a plane. As an application of the proposed technique a method of finding linear functional global extremum is described, including its use for systems with arbitrary dimensionality. Keywords Reachable set • Optimal control • Non-linear dynamic system 1 Introduction Reachable sets (RS) are among classical objects of investigation in the optimal control theory. The possibility to successfully operate with RS of controllable systems can greatly simplify the solutions of a number of traditional extreme problems, such as local and global search for a functional extremum, parametric identification, optimal control synthesis, system phase state estimation, control normalization, trajectories pencil control, and others. The problem of finding the RS is closely related to another classical problem of constructing integral funnels of differential inclusions [4

Advances in intelligent systems and computing, Dec 20, 2019

The paper considers numerical approaches for solving optimal control problems with free trajector... more The paper considers numerical approaches for solving optimal control problems with free trajectories at the end of the time interval. A modification of the algorithm of the conjugate gradient for studying the controlled dynamic problem is presented. The proposed technique has been tested by using the test optimal control problems. We describe the results of solving an applied problem of nanophysics. It is considered two cells of a quantum computer which are based on four tunnel-coupled semiconductor quantum dots. The multistage series of computations for investigation of system dependence from changes of the model parameters values are carried out and allowed to demonstrate the effectiveness of the proposed approach.

Communications in computer and information science, 2019

The paper considers a heuristic method for a global extremum search in an optimal control problem... more The paper considers a heuristic method for a global extremum search in an optimal control problem based on the idea of covering a reachable set by n-dimensional balls, including the built-in mechanisms for Lipschitz constant estimating of the objective functional. A step-by-step description of the coverage algorithm and the proposed method for generating start and auxiliary controls are presented. The proposed technique was used for solving applied optimal control problems: the problem of investment programs in Buryatia Republic and the problem of restoring the Black Lands in Kalmykia.

The paper presents an approach to the numerical study of the problems of finding a global extremu... more The paper presents an approach to the numerical study of the problems of finding a global extremum of multiextremal functions, based on the use of a parabolas algorithm. As local methods of onedimensional search, the methods of parabolic interpolation and the golden section are used. The numerical testing of modifications of the implemented approach using known non-convex functions has been carried out. The proposed technique has been applied to investigate a more complex optimization problem of a controlled dynamical power system. The obtained numerical results allowed us to demonstrate the efficiency of the proposed computational technology.

DEStech Transactions on Computer Science and Engineering, Feb 6, 2019

The paper describes a technology for the numerical investigation of nonlinear nonconvex optimal c... more The paper describes a technology for the numerical investigation of nonlinear nonconvex optimal control problems. This approach is based on the basin-hopping algorithm at the globalizing stage and the modified Nesterov's gully method at the stage of local extremum search. We present two applied problems solved by the proposed technique.

The paper presents a methodical approach to the construction of modern software systems, as well ... more The paper presents a methodical approach to the construction of modern software systems, as well as the creation of computing resources accessible via the Internet. The developed technologies are applied to solve the problem of legacy software using the example of the software OPTCON for solving optimal control problems.

Journal of Mathematical Sciences, Nov 1, 2022

Numerical Algebra, Control and Optimization, 2017

The main idea of the method consists in successive solving auxiliary problems, which minimizes a ... more The main idea of the method consists in successive solving auxiliary problems, which minimizes a special constructed Lagrange function, subject to linearized phase constraints. The linearly constrained auxiliary problems are more simple than the original ones because linear constraints can be easily processed. We shall discuss different aspects connected with approximating control problems and using the program system for solving them. We shall then pay attention to optimal control problems with constraints on inertia of control functions. For illustrations, four control problems will be solved using the proposed software.

Journal of Mathematical Sciences, Apr 23, 2019

We develop an algorithmic support for some classes of nonlinear optimal control problems. We prop... more We develop an algorithmic support for some classes of nonlinear optimal control problems. We propose several algorithms based on the first-and second order necessary conditions for solving optimal control problems with constraints on control. Efficiency of the algorithms is confirmed by solving various test and applied optimal control problems. Bibliography: 11 titles. Illustrations: 3 figures.