Caution in Iterative Modeling and Control Design

The Vinnicombe metric defining the gap between two plants, or two controllers, and its related robust stability results, are used as a tool to understand the need for cautious iterations (i.e. small controller modifications and, possibly, small model adjustments) that has been observed to be useful in iterative identification and control design. By the same token, these gap metric results allow one to compute controller updates that are smaller than would result from the optimal design based on the nominal design, and that guarantee stability of the actual closed loop system.