Search academic texts

Information × Registration Number 0222U003801, 0117U000473 , R & D reports Title Developing methods and algorithms of solving optimization problems on combinatorial configurations and trajectories of dynamic systems. popup.stage_title Head Donets Heorhii P., Доктор фізико-математичних наук Registration Date 30-05-2022 Organization V.M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine popup.description2 Object: the optimizatiоn problems on combinatorial configurations and trajectories of dynamic systems. Goal: to develop methods and algorithms for solving optimization problems on combinatorial configurations and trajectories of dynamic systems in conditions of conflict and uncertainty. Methods: combinatorics, graph theory, discrete optimization, mathematical theory of control, theory of set-valued mappings. Results: 1. For solving the extremal problems on combinatorial configurations, the methods and algorithms are created to construct graphs, representing given combinatorial configuration. 2. Methods of enumeration of configuration elements, their generation and comparison are developed to construct consequences with the help of one transposition of two elements. General scheme of directed structuring is developed to solve the optimization problems on combinatorial configurations. 3. Optimization problems on combinatorial configurations under (without) constraints are considered. 4. General schemes of algorithms to solve optimization combinatorial problems for the linear, fractional-linear and quadratic functions are worked out. 5. Methods and algorithms are created for control of dynamic systems in conditions of conflict and uncertainty. The rule of extremal aiming by M.M. Krasovskii is extended to the case of conflict-controlled processes, described by functional-differential systems. 6. The principle of time dilation is developed, which made it possible to solve the approach problems in the case when Pontryagins condition on the advantage in control resources does not hold. In particular, a number of problems of soft meeting for controlled second-order systems are solved. The results are new, not similar to the known. They can be used in financial and banking activities, in the optimization of business processes, in warfare, in aviation industry, to intercept controlled moving objects, to analyze conflict interactions for economic efficiency. Product Description popup.authors Biletsky Vasily I Donets Georgy Panasovych Kuzmenko Viktor M Chikrii Greta Ts., popup.nrat_date 2022-05-30 Close