Multi-Target Control Problems
Doyen, Luc; Quincampoix, Marc (1997), Multi-Target Control Problems, Journal of Optimization Theory and Applications, 93, 1, p. 121-139. http://dx.doi.org/10.1023/A:1022601901895
TypeArticle accepté pour publication ou publié
Journal nameJournal of Optimization Theory and Applications
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Abstract (EN)We study control problems with several targets in the case of nonlinear dynamic systems. The map associating with every initial condition the minimal time to reach successively two given targets is characterized in the framework of differential inclusions through the notion of viability kernel. This approach allows one to treat the problem without assumptions of regularity and to build numerical schemes computing the minimal time. We also study the problem where an order of visit of the targets is required. The statements are also extended to the case of p targets under state constraints. Equivalent formulations in terms of Hamilton–Jacobi equations are also provided.
Subjects / KeywordsControl theory; targets problems; differential inclusions; viability theory; Hamilton–Jacobi equations
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