Semiconcavity for the minimum time problem with time delay
speaker: Elisa Continelli (Università degli studi dell’Aquila)abstract: We analyze a minimum time problem with time delay and we investigate the regularity properties of the value function associated to the considered optimal control problem. In our setting, the minimum time function is no longer defined in a subset of Rn, as it happens when dealing with the undelayed case, but its domain is a subset of the Banach space C(−τ, 0; Rn). As far as the undelayed minimum time problem is concerned, it is known that, under suitable assumptions, the value function is semiconcave and it is a viscosity solution of an appropriate Hamilton- Jacobi-Belmann equation. Moreover, semiconcavity plays a prominent role in the derivation of some optimality conditions. For the value function of optimal control problems involving time delays, the Hamilton-Jacobi theory has been developed by many authors. Extending classical arguments, we are able to prove that, whenever a smallness assumption on the time delay size is required, the minimum time functional is Locally Lipschitz continuous and semiconcave with a linear moodulus in a suitable subset of the reachable set. Joint work with C. Pignotti.
timetable:
Wed 10 May, 10:10 - 10:40, Aula Dini
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