Controlled Ornstein-Uhlenbeck process with chance constraints

In Ref. 1, existence and optimality conditions were given for control systems whose dynamics are determined by a linear stochastic differential equation with linear feedback controls; moreover, the state variables satisfy probability constraints. Here, for the simplest case of such a model, the Ornstein-Uhlenbeck velocity process, we evaluate the necessary conditions derived in Ref. 1 and compute a time-optimal control such that a given threshold value > 0 is crossed with probability of at least 1 – .This work was supported by the Sonderforschungsbereiche 21 and 72, University of Bonn, Bonn, West Germany.