Robust Properties of Risk-Sensitive Control

Abstract.

The purpose of this paper is to characterize and prove robustness properties of risk-sensitive controllers precisely. In particular, we establish a stochastic version of the small gain theorem. This theorem is expressed in terms of an inequality which bounds the average output power in terms of the input power. Since this inequality is closely related to the risk-sensitive criterion, our stochastic small gain theorem can be expressed in terms of the risk-sensitive criterion. This provides a concrete motivation for the use of the risk-sensitive criterion stochastic robustness.