Research: Statistical Control

Statistical control is a type of stochastic optimal control where we view the cost function as a random variable and optimize function of the cost cumulants.  The first cost cumulant minimization corresponds to the celebrated linear-quadratic-Gaussian (LQG) control.  Thus, statistical control is a generalization of LQG methods.  Even though moments and cumulants are similar mathematically, in control engineering higher order cumulant control shows a great promise in contrast to cost moment control.  The word statistical is a substitute for the word cumulant because cumulants are commonly used in the statistical literature and researchers are more familiar with the word statistics than cumulants.  In this project, we investigate the characteristics of linear statistical control, develop nonlinear statistical control theory, study the relations between statistical control and dynamic game theory, and apply statistical control to various applications.

                               Figure 1: Effects of Cumulants on Cost Density Functions.