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Supervisory control of families of linear set-point controllers. I: Exact matching. (English) Zbl 0872.93009
This paper treats the first part of a work on supervisory control. A simply structured high-level controller (called a “supervisor”) is described. It is capable of switching into feedback with a single-input/single-output (SISO) process a sequence of linear positioning or set-point controllers from a family 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 candidate controllers would solve the positioning problem if the transfer function of the process were to be one of the subclasses’ members. Each subclass contains a “nominal process model transfer function” about which the subclass is centered. The supervisor effectuates a controller solution by (i) continuously comparing in real time suitably defined normed-squared output estimation errors or “performance signals” determined by the nominal process model transfer functions and (ii) by placing in the feedback loop from time to time the candidate controller whose corresponding performance signal is the smallest. It is shown that in absence of unmodeled process dynamics, the proposed supervisor can achieve a zero steady-state tracking error even if process disturbances are present, provided they are bounded and constant. A second paper (whose results are provided in this paper without proofs) shows that the same supervisor can perform its function also in the face of unmodeled process dynamics and moreover that none of the signals within the overall system can grow without bound in response to bounded disturbance or noise inputs, be they constant or not.

MSC:
93A13Hierarchical systems
93C73Perturbations in control systems
93C41Control problems with incomplete information