Towards dual robust nonlinear model predictive control: A multi-stage approach

This paper presents an approach to dual robust nonlinear model predictive control (NMPC). Dual control is traditionally formulated as a technique that seeks to solve the trade-off between probing actions, which result in a better estimation of the unknown parameters, and the optimal operation of the uncertain dynamic system. We propose a dual robust NMPC method based on the multi-stage approach that represents the uncertainty as a scenario tree of its possible realizations. We achieve a dual control formulation by taking explicitly into account the reduction of the uncertainty that future probing actions would provide over the prediction horizon. Using such formulation, our approach does not require any a priori decision on the relative importance of the probing actions with respect to the optimal operation of the system, as proposed in some recent approaches. The results obtained for a chemical engineering example show the advantages of using a dual NMPC approach based on multi-stage NMPC over the sequential use of parameter estimation with a posteriori approximation of the covariance of the parameter estimates.