Ensemble Control of Dynamic Systems with Square Impulses

• Type: Article in International Conference Proceedings Book
• Date: 2022

Authors

Staritsyn, M (Author) FEUP; Goncharova, E (Author) Other; Pereira, FL (Author) Other

Conference proceedings International

Title: IFAC PAPERSONLINE

Pages: 242-247

10th Vienna International Conference on Mathematical Modelling (MATHMOD)

Tech Univ Wien, ELECTR NETWORK, JUL 27-29, 2022

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Other information

Authenticus ID: P-00X-8J5

DOI: 10.1016/j.ifacol.2022.09.031

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