Cumulant control of discrete time linear stochastic systems

Traditionally, feedback regulator control laws for linear stochastic systems have been achieved by minimization of the mathematical expectation of a particular quadratic performance measure. Over the past decade some research efforts have been directed at the generalization of this class of problems to include higher-order statistical indices, involving mean-conditional-cumulants of the quadratic performance measure. However, these efforts, which were made in the continuous time case, have not yielded a complete generalization.

In this work such a generalization is achieved. The key question addressed involves enforcement of an "admissibility" constraint on the set of control actions over which optimization is carried out. This constraint assures that the control actions will be physically realizable and determined by feedback control laws. The main result of this work is the discovery of an equivalent optimization problem where the admissibility constraint is not present.