Adaptive controllers with explicit and implicit reference models and stochastic self tuning regulators-eqivalence and duality aspects

It is shown in this paper that : 1) The Minimum Variance Self Tuning Regulators and a configuration of Adaptive Controllers with Implicit (or Explicit) Reference Model feature an asymptotic duality character which extends the duality existing in the linear case with known parameters between the minimum variance control and the modal control. 2) Adaptive Control with an Explicit Reference Model is equivalent to an Adaptive Control with an Implicit Reference Model using an intermediate adaptive predictor, if the adaptive predictor plus the control behave like the explicit reference model. 3) The result of 1) is generalized by considering the asymptotic duality between Model Reference Adaptive Controllers and the class of Stochastic self Tuning Regulators which contains the self tuning minimum variance regulator as a particular case.