The Mayer and Minimum Time Problems with Stratified State Constraints
- 30 Downloads
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
Unable to display preview. Download preview PDF.
- 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