A control problem in a manifold with nonsmooth boundary
A control problem in a manifold with nonsmooth boundary
- Neue Suche nach: Boel, R.
- Neue Suche nach: Kohlmann, M.
- Neue Suche nach: Boel, R.
- Neue Suche nach: Kohlmann, M.
Abstract Diffusions in manifolds with non-smooth boundaries (e.g. in R + r × Rn-n) often arise as approximations to queueing networks. We consider the following stochastic differential equation : where wt is a Brounian motion, l t i the local time at {xi = 0} and m t i a Brounian motion at the time scale l t i . We first prove existence of weak solutions to this s.d.e. A Ginsanov theorem modifying the drift f inside the domain and the average angle of reflection ai on the boundary {xi = 0} will be proved. Using this thearem we can allow f and ai to depend on a full information control law u(t,θ). A reasonable cost structure then assigns extra cost for hitting the boundaries {xi = 0}. So, on the one hand we can control the behaviour around the boundary via the average angle of neflection ai(x,u), on the other hand we penalize the system for being close to this boundary. This leads to a well-posed optimal control problem, with dynamic programming type optimality conditions and existence theorems under fainly standard — but strict — assumptions.
Dokumentinformationen
A control problem in a manifold with nonsmooth boundary
1982-01-01
22 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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