On adaptive minimum variance regulation for non-minimum phase plants

Adaptive minimum variance control is applied to nonminimum phase plants augmented with adaptive compensators. The objective of the compensators is to achieve, asymptotically, a minimum phase property for the augmented plant. With this property, the minimum variance controller gives a stabilizing control signal. The scheme proposed has interpretations as an adaptive quadratic index minimizing procedure and also as an adaptive pole assignment algorithm. The advantage over other adaptive quadratic index minimizing procedures is simply that the weightings are made adaptive so as to guarantee convergence. One feature not shared by other adaptive pole assignment schemes is that they conveniently specialize to simple minimum variance schemes when, for these, control energy constraints are not violated. This paper presents only the discrete-time adaptive regulator version. Companion papers give a full global convergence theory and pre-processing augmentations for the stochastic tracking scheme versions.