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Minimum energy control of degenerate Cauchy problem with skew-Hermitian pencil

Minimum energy control of degenerate Cauchy problem with skew-Hermitian pencil AbstractThe present research paper deals with the effectiveness of the control of an infinite-dimensional degenerate Cauchy problem with variable operator coefficients, skew-Hermitian pencil and bounded input condition. This study explores the minimum energy control problem. The investigation follows a set of methods to examine the procedure for developing a new result to solve the problem. Indeed, by the use of decomposition transformation of the considered system and the application of the Gramian operator, the formula of the process for controlling the system with minimum energy is obtained. Afterwards, a procedure to compute the optimal input for minimizing the performance index is then proposed. In a nutshell, the obtained results indicate that optimal control for minimizing the performance index ensures the solution of the minimum energy control of an infinite-dimensional degenerate Cauchy problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Analysis de Gruyter

Minimum energy control of degenerate Cauchy problem with skew-Hermitian pencil

Journal of Applied Analysis , Volume 28 (2): 11 – Dec 1, 2022

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Publisher
de Gruyter
Copyright
© 2022 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6082
eISSN
1869-6082
DOI
10.1515/jaa-2021-2077
Publisher site
See Article on Publisher Site

Abstract

AbstractThe present research paper deals with the effectiveness of the control of an infinite-dimensional degenerate Cauchy problem with variable operator coefficients, skew-Hermitian pencil and bounded input condition. This study explores the minimum energy control problem. The investigation follows a set of methods to examine the procedure for developing a new result to solve the problem. Indeed, by the use of decomposition transformation of the considered system and the application of the Gramian operator, the formula of the process for controlling the system with minimum energy is obtained. Afterwards, a procedure to compute the optimal input for minimizing the performance index is then proposed. In a nutshell, the obtained results indicate that optimal control for minimizing the performance index ensures the solution of the minimum energy control of an infinite-dimensional degenerate Cauchy problem.

Journal

Journal of Applied Analysisde Gruyter

Published: Dec 1, 2022

Keywords: Minimum energy control; exact controllability; optimal control; skew-Hermitian pencil; bounded input; performance index; 93D25; 93B05; 15B57; 34L99

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