Minimum time problem with impulsive and ordinary controls
| Autor: | Monica Motta |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
0211 other engineering and technologies
Convex set Hamilton Jacobi equations 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Convexity Combinatorics Discrete Mathematics and Combinatorics 0101 mathematics Existence of optimal controls Impulsive optimal control problems Lavrentiev phenomenon Lower semicontinuous viscosity solutions Analysis Applied Mathematics Mathematics 021103 operations research Degenerate energy levels Minimum time State (functional analysis) Absolute continuity Minimum time function ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Affine transformation |
| Zdroj: | Discrete & Continuous Dynamical Systems - A. 38:5781-5809 |
| ISSN: | 1553-5231 |
| DOI: | 10.3934/dcds.2018252 |
| Popis: | Given a nonlinear control system depending on two controls \begin{document}$u$\end{document} and \begin{document}$v$\end{document} , with dynamics affine in the (unbounded) derivative of \begin{document}$u$\end{document} and a closed target set \begin{document}$\mathcal{S}$\end{document} depending both on the state and on the control \begin{document}$u$\end{document} , we study the minimum time problem with a bound on the total variation of \begin{document}$u$\end{document} and \begin{document}$u$\end{document} constrained in a closed, convex set \begin{document}$U$\end{document} , possibly with empty interior. We revisit several concepts of generalized control and solution considered in the literature and show that they all lead to the same minimum time function \begin{document}$T$\end{document} . Then we obtain sufficient conditions for the existence of an optimal generalized trajectory-control pair and study the possibility of Lavrentiev-type gap between the minimum time in the spaces of regular (that is, absolutely continuous) and generalized controls. Finally, under a convexity assumption on the dynamics, we characterize \begin{document}$T$\end{document} as the unique lower semicontinuous solution of a regular HJ equation with degenerate state constraints. |
| Databáze: | OpenAIRE |
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