Pruning and merging strategies in receding horizon bicriterial dual controller with multiple linearization

The receding horizon bicriterial dual controller for a discrete linear system with non-Gaussian random quantities is presented and its properties are discussed. The controller is designed by employing two criteria that reflect the need to respect the conflicting purposes of the dual control, the caution and probing. The cautious part of the control is designed using the receding horizon type of the criterion in order to prevent the myopic behavior of the controller. As the random quantities are modeled as Gaussian sums (GS), the Gaussian sum estimation method (GSM) is applied. It will be shown that owing to the nonlinear character of the control law it is advantageous to determine the probing separately for each local estimate that constitute elements of the GS of augmented state estimate. The use of GSM has one drawback stemming from the fact that the number of terms in sum grows exponentially with time. Various pruning techniques will be discussed and their influence on the quality of the resulting control will be presented in an example.