On the Optimality of Certainty Equivalence for Adaptive Model Reference Control

Most implementations of adaptive model reference control employ a certainty equivalence assumption whereby at each step, identification is performed first and then a control is devised by treating parameter estimates as if they were the correct values. Using certainty equivalence has often led to an acceptable control but has been without theoretical justification. This paper demonstrates that for a class of adaptive model reference controllers, the optimal (in a minimax sense) one-step-ahead control will either be zero or the certainty equivalence control.