Robust Statistical Controller for Stochastic Systems

Abstract

The statistical control scheme presented here involves obtaining a feedback law which minimizes the value of a finite linear combination of the first k th cost cumulants of a traditional integral quadratic cost associated with a linear stochastic system. This statistical control scheme has shown to be quite competitive with other modern control design paradigms for several benchmark problems. This paper focuses on a particular type of statistical control known as the infinite horizon output feedback statistical control where an arbitrarily large time horizon is considered, not all the system state information is available, and the unmeasured states are estimated using the Kalman filter. Design of the statistical controller requires the precise knowledge of system parameters and system uncertainties could severely degrade the performance or even destabilize the controlled system. The main objective of this paper is to extend the existing infinite horizon output feedback statistical control theory to a class of linear time-invariant stochastic systems with structured uncertainty. This paper presents a computationally feasible algorithm for the construction of the robust statistical control scheme which guarantees the stability of the controlled system.