Optimal Controllers for Nonsymmetric and Nonquadratic Loss Functions

Minimum-variance controllers provide an essential link for integrating concepts of statistical process control and engineering process control. These controllers are specifically designed to minimize a quadratic loss function. In some problems, however, other loss functions may be more appropriate. In this article, controllers that are optimal for nonsymmetric and nonquadratic loss functions are derived. In many cases, these controllers retain the basic simplicity of the minimum-variance controller. Additionally, for process disturbances driven by normal white noise, the minimum-variance controller is shown to be optimal for a broad class of objective functions.