Online Control of Process Variance Using Feedback

For many stochastic control problem formulations, design objectives typically include constraining the covariance of the outputs of the system. Recent engineering challenges have demonstrated an interest in controlling system output covariances to a setpoint. However, open-loop control of system output covariance can be exceptionally challenging when the system has significant plant uncertainties. This paper explores closed-loop control of the system's output covariance using a windowed variance function. The stochastic nature of the windowed variance feedback means that root locus and other classical control design techniques cannot be immediately used. Expected value analysis is used to generate transfer functions for the average response of such systems, and the results are used to design controllers. Stochastic simulations are presented to verify the analytical results and make other observations concerning closed-loop variance control.