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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Nonlinear Differential Equations and Applications NoDEA
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
