Certainty equivalence and the minimax principle in self-tuning control

The majority of the published treatments of self-tuning controllers 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. This note demonstrates that when knowledge of parameter estimate uncertainty is used to minimize the maximum one-step-ahead cost, the optimal regulator gains for a class of self-tuning regulators will be either zero or the certainty equivalence gain.