Supervisory control of families of linear set-point controllers

This paper describes a simple, `high-level´ controller called a `supervisor´ which is capable of switching into feedback with a SISO process, a sequence of linear positioning or set-point controllers from a family ℱ_C of candidate controllers, so as to cause the output of the process to approach and track a constant reference input. The process is assumed to be modeled by a SISO linear system whose transfer function is in the union of a number of subclasses, each subclass being small enough so that one of the controllers in ℱ_C would solve the positioning problem, were the process´s transfer function to be one of the subclasses members. The supervisor decides which controller to put in feedback with the process, not by an exhaustive search-i.e., by experimentally evaluating each and every candidate controller´s performance by briefly applying it to the process-but rather by continuously comparing in real time suitably defined `output estimation errors´ generated by the candidate controllers, whether or not they are in feedback with the process. It is shown that under reasonably mild conditions, the supervisor can successfully perform its function in spite of modeling errors, provided the errors are sufficiently small. It is also shown that the supervisor will invariably correctly classify the process in finite time, so long as the reference input is nonzero and the “dc gains” of the “nominal” candidate process model transfer functions are distinct