Minimum energy control of degenerate Cauchy problem with skew-Hermitian pencil
-
Meriem Benaoued
and
Djillali Bouagada
Abstract
The 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.
Funding statement: This paper presents research results of the ACSY Team (Analysis & Control systems team) and of the doctoral training on the Operational Research and Decision Supported funded by the General Directorate for Scientific Research and Technological Development of Algeria (DGRSDT) and supported by University of Mostaganem Abdelhamid Ibn Badis (UMAB) and initiated by the concerted research project on Control and Systems Theory (PRFU Project Code: C00L03UN270120200003).
Acknowledgements
The authors would like to express their sincere thanks to the referees for their valuable suggestions that greatly enhanced the quality of this paper.
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- Frontmatter
- Estimates for a beam-like partial differential operator and applications
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- Analyzing the existence of solution of a fractional order integral equation: A fixed point approach
- Existence of solution to a nonlocal biharmonic problem with dependence on gradient and Laplacian
- Global existence and exponential decay for a viscoelastic equation with not necessarily decreasing kernel
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- Splines in vibration analysis of non-homogeneous circular plates of quadratic thickness
- The weak eigenfunctions of boundary-value problem with symmetric discontinuities
- Some subclasses of analytic functions involving certain integral operator
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