Certainty equivalence implies detectability

It is shown that any stabilizing, certainty equivalence control used within an adaptive control system, causes the familiar interconnection of a contr olled process and associated output estimator to be detectable through the estimator's output error e(p), for every frozen value of the index or param eter vector p upon which both the estimator and controller dynamics depend. The fact that certainty equivalence implies detectability has been known f or some time - this has been shown to be so whenever the process model is l inear and the controller and estimator models are also linear for every fro zen value of p. In this paper, use is made of recently introduced concepts of input-to-state stability and detectability for nonlinear systems to prov e that the same implication is valid in a more general, nonlinear setting. (C) 1999 Published by Elsevier Science B.V. All rights reserved.