An Adaptive Model Predictive Dual Controller

We present a novel adaptive explicit dual controller based on model predictive control (MPC). The adaptive control algorithm is designed to handle poorly identified models and is able to excite the system so that sufficient information can be gathered for proper identification. This excitation is achieved without requiring the input to be persistently exciting; rather, the excitation objective is formulated such that excitation takes place only in the absence of sufficiently informative data, while a trade-off between excitation and output regulation is maintained. The algorithm is an extension of a standard MPC design and can easily be implemented with minor modifications to an existing MPC. As an example we consider a first-order linear plant which causes other controllers to fail when identified poorly. We show that our proposed algorithm correctly estimates the system parameters in the minimal time possible and then prioritizes directing the output to zero while maintaining minimal excitation.