Abstract
We study a space-time extension of the notion of solution to a nonlinear control system with unbounded controls (in the form of derivatives) and state constraints. A natural motivation is provided by minimum problems, where the presence of unbounded controls together with the lack of any coercivity assumption may give rise to minimizing sequences of trajectories which converge to discontinuous maps. The main problem focused on in this paper can be summarized as follows: is the proposed extension a proper extension? Which means: is one able to approximate an extended trajectory with ordinary ones? When the system is subject to a state constraint the answer is generally negative. On the other hand, we prove that under suitable conditions on the vectogram at the boundary points of the constraint set the extension turns out to be proper.
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More From: Nonlinear Differential Equations and Applications NoDEA
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