Two evasion problems in a plane with separate controls and non-convex terminal sets |
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| Affiliation: | 1. Munzur University, Department of Industrial Engineering, 62000, Tunceli, Turkey;2. Antalya Bilim University, Department of Industrial Engineering, Antalya, Turkey;1. Post Graduate Program of Production Engineering, UFRGS, Brazil;2. Federal Institute of Education, Science and Technology of Rio Grande do Sul – Campus Porto Alegre, Brazil;1. Centre for Research & Development in Mechanical Engineering (CIDEM), School of Engineering of Porto (ISEP), Polytechnic of Porto, 4200-072, Porto, Portugal;2. Algoritmi Centre, School of Engineering, University of Minho, Guimarães, Portugal;3. Research Centre on Environment and Health, Department of Environmental Health, School of Health of Polytechnic Institute of Porto, Porto, Portugal;1. Department of Occupational Hygiene, School of Public Health and Research, Center for Health Sciences, Hamadan University of Medical Sciences, Hamadan, Iran;2. Department of Occupational Hygiene, School of Public Health, Hamadan University of Medical Sciences, Hamadan, Iran;3. Department of Management, University of Tehran, Tehran, Iran;4. Department of Health Management, School of Public Health, Hamadan University of Medical Sciences, Hamadan, Iran;5. Department of Biostatistics, School of Public Health, Hamadan University of Medical Sciences, Hamadan, Iran |
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| Abstract: | Two different pursuit-evasion games are considered from the evader's point of view. The phase space is a plane, each of the two players controlling the motion of a point only along its own coordinate. The terminal sets are not convex; in the first problem, the set is an arc of a circle, in the second, the union of tow segments. In both games evasion cannot the achieved by means of programmed controls, but it can be achieved using feedback control. However, the strategies, which are continuous functions of the phase vector, have different properties in each problem. In the first, they cannot guarantee evasion (which is typical for the linear-convex case as well), but in the second they can (which is impossible in linear-convex games with a fixed final time). Verification that evasion is unachievable using such strategies reduces here to proving the solvability of a certain initial-value problem for an advanced differential equation, to which the Schauder principle is applicable. |
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