Semi-receding horizon algorithm for “sufficiently exciting” MPC with adaptive search step

In this paper, the task of finding an algorithm providing sufficiently excited data within the MPC framework is tackled. Such algorithm is expected to take action only when the re-identification is needed and it shall be used as the “least costly” closed loop identification experiment for MPC. The already existing approach based on maximization of the smallest eigenvalue of the information matrix increase is revised and an adaptation by introducing a semi-receding horizon principle is performed. Further, the optimization algorithm used for the maximization of the provided information is adapted such that the constraints on the maximal allowed control performance deterioration are handled more carefully and are incorporated directly into the process instead of using them just as a termination condition. The effect of the performed adaptations is inspected using a numerical example. The example shows that the employment of the semi-receding horizon brings major improvement of the identification properties of the obtained data and the proposed adaptive-search step algorithm used for the “informativeness” optimization brings further significant increase of the contained information while the aggravation of the economical and tracking aspects of the control are kept at acceptable level.