Construction of the viability kernel for a generalized dynamical system |
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| Institution: | 1. Institute of Mathematics and Computer Sciences, Ural Federal University, 620000, Lenina, Ekaterinburg, 51, Russia;2. Department of Physics and Chemistry, Group of Interdisciplinary Theoretical Physics, Universitá degli Studi di Palermo and CNISM, Viale delle Scienze, Edificio 18, Palermo I-90128, Italy;3. Radiophysics Department, National Research Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, Nizhni Novgorod 603950, Russia;4. Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 64, Catania I-90123, Italy;1. Mathworks, MA USA;2. Purdue University, West Lafayette, IN USA |
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| Abstract: | The problem of the approximate construction of the viability kernel for a generalized dynamical system, the evolution of which is specified directly by an attainability set, is investigated under phase constraints. A backward grid method, based on the substitution of the phase space by pixels and a consideration of “inverse” attainability sets, is proposed. The convergence of the method is proved. |
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