Abstract
This paper considers some aspects of Krasovsky-Subbotin’s item which is well-known as a stable bridge. It is shown that the Lipschitz condition for the right-hand side function of the initial differential equation is essential for the alternative theorem (see [13]) if the problems are solved in the class of measurable strategies. The measurable strategies are defined as measurable feedback controls. Necessary and sufficient conditions are given for keeping the solutions of the controlled differential system in the values of upper semi-continuous multi-function. These kind of problems are related to the viability theory (see [6]–[12]) and to the conflict controlled systems theory (see [13]–[16]).
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Ivanov, R.P. (1991). Stable Graphs of Multi-Functions in Conflict Controlled Systems. In: Di Masi, G.B., Gombani, A., Kurzhansky, A.B. (eds) Modeling, Estimation and Control of Systems with Uncertainty. Progress in Systems and Control Theory, vol 10. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0443-5_12
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DOI: https://doi.org/10.1007/978-1-4612-0443-5_12
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