Linear Cumulant Control and Its Relationship to Risk-Sensitive Control

Matrix differential equation descriptions of the cumulants of an integral quadratic cost associated with a linear system with white-noise input were derived in the mid-70s using generalized Karhunen-Loeve expansion techniques. Here, these same descriptions are derived directly from the cumulant generating function of the cost. A generalization of the k-cumulant control problem class introduced in 1998 is also presented. The solution to this more general class of optimal cumulant control problems is given, and the risk sensitive control problem of optimizing the cumulant generating function of the LQG cost is shown to be included in this cumulant control class.