RISK-SENSITIVE AND ROBUST ESCAPE CRITERIA

The problem of controlling a noisy process so as to prevent it from le aving a prescribed set has a number of interesting applications. In th is paper, new approaches to this problem are considered. First, a risk -sensitive criterion for a stochastic diffusion process model is exami ned, and it is shown that the value is a classical solution of a relat ed PDE. The qualitative properties of this criterion are favorably con trasted with those of existing criteria in the risk-averse limit. It i s proved that in the risk-averse limit the value of the risk-sensitive criterion converges to a viscosity solution of a first-order PDE. It is then demonstrated that the value function of a deterministic differ ential game is also a viscosity solution to the PDE. This game gives a robust control formulation of the escape time problem and is analogou s to H-infinity control. In particular, the opposing player attempts t o push the process out of the prescribed set and suffers an L-2 cost f or his efforts. Lower bounds on the escape time as a function of this cost are obtained.