Abstract
The problem of existence of a regular synthesis for the linear time-optimal control problem with convex control constraints is studied. A regular synthesis on the whole reachable set cannot be established for this problem by direct use of Brunovsky’s general existence theorem. This is in accord with the example of a nonsubanalytic reachable set due to Lojasiewicz and Sussmann [S. Lojasiewicz, Jr. and H. J. Sussmann, “Some examples of reachable sets and optimal cost functions that fail to be subanalytic,” SIAM J. Control Optim., 23 (1985), pp. 584–598]. A closed subset H of the reachable set K that has Lebesgue measure zero is constructed and the existence of a regular synthesis on $K - H$ is proved.
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 callDisclaimer: 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.
