Persistent excitation condition within the dual control framework

Model Predictive Control framework is currently used in many different fields of expertise. The inherent part and very often also the main bottleneck is the model of a process used for the computation of predictions.Due to many reasons e.g. ageing, from time to time there exists a need to adjust/re-identify (if there was already some kind of a model-based controller) or to construct a brand new model (in other cases). Frequently, the process generating the data is under some kind of control, imposing thus problems when classical open loop identification methods are considered. The need for models identified from the data gathered in a closed-loop fashion and a request for possible re-identification of the model parameters lead to the emerge of dual control where the problems of control and system identification are addressed simultaneously.In this paper, we present a new algorithm based on the persistent excitation condition when the minimal eigenvalue of the information matrix is maximized in order to have sufficiently exciting optimal control signal satisfying the control requirements.