Olinjär stokastisk reglering av extremvärden

Abstract: In this report discrete time optimal control of extreme values are investigated. Both the full information case and partial information case are discussed. There has been payed special attention to numerical solution of the Bellman equation. For a special full information case the optimal controller has been obtained by a numerical solution. This controller has been compared with the minimal variance controller and the linear minimal upcrossing controller through simulations. It is seen that the optimal controller performs better than the linear controllers when the noise is high and the minimization horizon is short. Further, the optimal controller has been compared with the non-linear minimal upcrossing controller, which has been derived without using Bellman's equation. It is seen that the controllers were almost identical for the case studied, and for a special case it is shown that they are identical.