Abstract
We consider a nonlinear control system involving a maximal monotone map and with a priori feedback. We assume that the control constraint multifunction \(U(t,x)\) is nonconvex valued and only lsc in the \(x \in \mathbb{R}^{N}\) variable. Using the Q-regularization (in the sense of Cesari) of \(U(t,\cdot )\), we introduce a relaxed system. We show that this relaxation process is admissible.
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The authors wish to thank the two knowledgeable referees for their corrections and important remarks.
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Papageorgiou, N.S., Vetro, C. & Vetro, F. Relaxation for a Class of Control Systems with Unilateral Constraints. Acta Appl Math 167, 99–115 (2020). https://doi.org/10.1007/s10440-019-00270-4
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DOI: https://doi.org/10.1007/s10440-019-00270-4
Keywords
- Q-regularization
- Lower semicontinuous multifunction
- Admissible relaxation
- Maximal monotone map
- Continuous selection