Risk-sensitive control with HARA utility

In this paper, a control methodology based on the hyperbolic absolute risk averse (HARA) utility function is presented as an alternative to the exponential-of-an-integral approach to finding robust controllers. This work is inspired by the intuition that HARA controllers, while being robust, may give better performance than exponential controllers in normal situations. The HARA problem is shown to be equivalent to a certain differential game, and the asymptotic properties of the HARA problem and this differential game are studied. As an example, a linear-quadratic HARA problem is studied, where the problem of finding a robust HARA controller is proved to be equivalent to solving a standard linear-quadratic problem for a system with a higher noise intensity. This reveals an interesting relationship between robustness and uncertainty.