Statistical Control of Stochastic Systems Incorporating Integral Feedback: Performance Robustness Analysis

Summary

An innovative paradigm for statistical approximation is presented to evaluate performance measure statistics of a class of stochastic systems with integral control. This methodology, which makes use of both compactness from the logic of the state-space model description and quantitativity from the probabilistic knowledge of stochastic disturbances, now allows us to predict more accurately the effect of a chi-squared random variable on the performance uncertainty of the stochastic system with both state feedback and integral output feedback. It is shown that the computational method detailed herein is able to calculate the exact statistics of the performance measure of any orders which are then utilized in the design of an optimal statistical control solution to effectively address the unresolved challenge of closed-loop performance robustness without massive Monte Carlo simulations.