Will the self-tuning approach work for general cost criteria? (Q1063566)

The paper deals with linear stochastic systems. Especially, it studies the self-tuning procedure for adaptive control. A cost criterion measuring the performance of the unknown system is considered. If the cost criterion is anything else than a minimum (output) variance criterion, then the procedure of estimating the unknown parameters of the linear system and then applying a control input which is optimal for the given cost criterion and the parameter estimates, will not self-tune to the optimal control law. An exception to this is the class of systems with a large enough delay. However, this case is discussed separately.