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Ensemble Control of Dynamic Systems with Square Impulses

Title
Ensemble Control of Dynamic Systems with Square Impulses
Type
Article in International Conference Proceedings Book
Year
2022
Authors
Staritsyn, M
(Author)
FEUP
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Goncharova, E
(Author)
Other
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Pereira, FL
(Author)
Other
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Conference proceedings International
Pages: 242-247
10th Vienna International Conference on Mathematical Modelling (MATHMOD)
Tech Univ Wien, ELECTR NETWORK, JUL 27-29, 2022
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Authenticus ID: P-00X-8J5
Abstract (EN): In the article, the basic mathematical concepts of quadratic-impulse control are extended to dynamical systems in the space of probability measures (local continuity equations) representing dynamic ensembles of (infinitely many) homotypic individuals. Starting from a model with quadratic dependence on an unbounded control, we constructively design its impulsive trajectory extension, which, as a byproduct, ensures also the well-posedness of an associated optimal control problem. The main attention is paid to the characteristic control ODE whose extension combines a discontinuous time change with a convexification of the velocity set via generalized controls. Finally, we show that it is possible to exclude the generalized controls and represent extended states as impulsive solutions of a measure-driven ODE. The resulting impulsive continuity equation can be viewed as a measure-driven equation in the space of measures. Copyright (C) 2022 The Authors.
Language: English
Type (Professor's evaluation): Scientific
No. of pages: 6
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