The Mayer and Minimum Time Problems with Stratified State Constraints
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This paper studies optimal control problems with state constraints by imposing structural assumptions on the constraint domain coupled with a tangential restriction with the dynamics. These assumptions replace pointing or controllability assumptions that are common in the literature, and provide a framework under which feasible boundary trajectories can be analyzed directly. The value functions associated with the state constrained Mayer and minimal time problems are characterized as solutions to a pair of Hamilton-Jacobi inequalities with appropriate boundary conditions. The novel feature of these inequalities lies in the choice of the Hamiltonian.
KeywordsState constraints Stratified structure Mayer problem Minimal time function Hamilton-Jacobi equations
Mathematics Subject Classification (2010)35B37 49J15 49Lxx 49J53 90C39
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The authors would like to thank the editor and the anonymous referees for their useful comments and suggestions. This work was partially supported by iCODE institue, the European Union under the 7th Framework Programme FP7-PEOPLE-2010-ITN Grant agreement number 264735-SADCO and by the ANR project HJNet ANR-12-BS01-0008-01.
- 12.Clarke, F.: Functional analysis, calculus of variations and optimal control. Volume 264 of Graduate Text in Mathematics. Springer (2013)Google Scholar
- 13.Clarke, F., Ledyaev, Y., Stern, R., Wolenski, P.: Nonsmooth Analysis and Control Theory. Volume 178 of Graduate Text in Mathematics. Springer (1998)Google Scholar
- 23.Lee, J.: Introduction to smooth manifolds. Volume 218 of Graduate Text in Mathematics. Springer (2013)Google Scholar
- 28.Smirnov, G.: Introduction to the theory of differential inclusions. Volume 41 of Graduate Studies in Mathematics. AMS (2002)Google Scholar