Divination of closed-loop stability and performance via frequency response function estimates

With knowledge of the internal stability of a closed-loop system with an unknown plant PP and a known controller C1C1, the stability and performance of another closed-loop system with the same PP and a known candidate controller C2C2 are divined without constructing the (P,C2)(P,C2) loop. This is performed through nonparametric identification of the frequency response functions of PP or other transfer functions, based on a limited amount of signal data collected from experiments on the internally stable (P,C1)(P,C1) closed-loop system excited by designed reference signals and corrupted by disturbances. An error analysis is provided and conditions for the reliable assessment of stability and performance are characterized. Linkages with the works of others in controller validation, certification, and unfalsification are studied and connections to system identification for control are explored, notably in the treatment of deliberate experiments and assumptions in moving from unfalsification to divination.