The Mayer and Minimum Time Problems with Stratified State Constraints

C. Hermosilla, Peter R. Wolenski and Hasnaa Zidani
2017
Publication type:
Paper in peer-reviewed journals
Journal:
Set-Valued and Variational Analysis
Publisher:
Springer
Keywords :
Mayer problem; stratified structure; minimal time function; Hamilton-Jacobi equations; State constraints;
Abstract:
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.
BibTeX:
@article{Her-Wol-Zid-2017,
    author={C. Hermosilla and Peter R. Wolenski and Hasnaa Zidani },
    title={The Mayer and Minimum Time Problems with Stratified State 
           Constraints },
    doi={10.1007/s11228-017-0413-z },
    journal={Set-Valued and Variational Analysis },
    year={2017 },
}