Optimal Identification Time for Control

This paper deals with consecutive (open-loop) identification and (closed-loop) control of a linear, time-invariant SISO process. The partition of a fixed total time between identification and control. is optimised according to an LQ criterion. For a static gain process, an analytical expression for the optimal identification time as a function of the a-priori parameter mean and variance is derived. For an integrator process, the optimal identification time obtained from simulations is approximated by an analytical formula. Both procedures are applied on-line by replacing the a-priori statistics by their estimates. Finding an analytical expression for higher order processes appeared infeasible. Therefore, for a static gain process, at each sampling instant, the predicted cost for continuing identification is compared to the predicted cost for starting control This procedure is expected to be applicable for dynamic systems of high order.