Abstract
We consider systems of controlled parabolic equations, coupled in lower-order terms, where the controllers act in a subdomain. We prove results of feedback stabilization to given nonstationary solutions satisfying some boundedness conditions. The argument relies on some refined estimates of the cost of approximate controllability and on the study of an appropriate differential Riccati equation.
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Acknowledgments
This work was supported by Grant PN-II-ID-PCE-2012-4-0456 of the Romanian National Authority for Scientific Research and Innovation, CNCS–UEFISCDI.
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Communicated by Firdaus E. Udwadia.
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Lefter, CG. Internal Feedback Stabilization of Nonstationary Solutions to Semilinear Parabolic Systems. J Optim Theory Appl 170, 960–976 (2016). https://doi.org/10.1007/s10957-016-0964-4
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DOI: https://doi.org/10.1007/s10957-016-0964-4
Keywords
- Systems of parabolic equations
- Approximate controllability
- Feedback stabilization
- Riccati differential equation