Robust nonlinear model predictive control with reduction of uncertainty via dual control

Dual control is a technique that solves the tradeoff between using the input signal for the excitation of the system excitation signal (probing actions) and controlling it, which results in a better estimation of the unknown parameters and therefore in a better (tracking or economic) performance. In this paper we present a dual control approach for multistage robust NMPC where the uncertainty is represented as a tree of possible realizations. The proposed approach achieves implicit dual control actions by considering the future reduction of the ranges of the uncertainties due to control actions and measurements. The region of the uncertainties is described by the covariance of the parameter estimates. The proposed scheme does not require a priori knowledge on the relative importance of the probing action compared to the optimal operation of the system, as employed in other approaches. Simulation results obtained for a semi-batch reactor case study show the advantages of dual NMPC over robust (multi-stage) NMPC and adaptive robust NMPC, where the scenario tree is updated whenever a new measurement information is available.