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Exact controllability of linear mean‐field stochastic systems and observability inequality for mean‐field backward stochastic differential equations

Exact controllability of linear mean‐field stochastic systems and observability inequality for... This paper is concerned with the exact controllability of linear mean‐field stochastic systems with time‐variant random coefficients. We prove that the exact controllability, the validity of the observability inequality for the dual equation, the unique solvability of a family of optimal control problems, the unique solvability of a family of mean‐field forward‐backward stochastic differential equations (MF‐FBSDEs), and the unique solvability of a family of norm optimal control problems are all equivalent. Therefore, some approaches are provided to investigate the issue of exact controllability. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Asian Journal of Control Wiley

Exact controllability of linear mean‐field stochastic systems and observability inequality for mean‐field backward stochastic differential equations

Asian Journal of Control , Volume 24 (1) – Jan 1, 2022

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References (35)

Publisher
Wiley
Copyright
© 2022 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd
ISSN
1561-8625
eISSN
1934-6093
DOI
10.1002/asjc.2443
Publisher site
See Article on Publisher Site

Abstract

This paper is concerned with the exact controllability of linear mean‐field stochastic systems with time‐variant random coefficients. We prove that the exact controllability, the validity of the observability inequality for the dual equation, the unique solvability of a family of optimal control problems, the unique solvability of a family of mean‐field forward‐backward stochastic differential equations (MF‐FBSDEs), and the unique solvability of a family of norm optimal control problems are all equivalent. Therefore, some approaches are provided to investigate the issue of exact controllability.

Journal

Asian Journal of ControlWiley

Published: Jan 1, 2022

Keywords: exact controllability; forward‐backward stochastic differential equation; mean‐field stochastic system; norm optimal control; observability inequality

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