Dual robust nonlinear model predictive control: A multi-stage approach

Abstract Dual control seeks to explicitly deal with the trade-off between the excitation of the controlled system by probing actions, which lead to a more accurate estimation of the unknown parameters of the plant model, and performance (set-point tracking, economic optimality, etc.) of the controlled system under the imperfect knowledge of the plant behavior. This paper presents a dual-control approach that extends a nonlinear model predictive controller, the control actions of which are robust against the effect of model uncertainties. The robustness is achieved via the multi-stage approach that uses a scenario-tree representation of the propagation of the uncertainties over the prediction horizon of the controller and includes the adaptation of the control actions on the basis of the information that is gained in the future in the optimization problem. The dual-control aspect of the proposed scheme is realized via the direct consideration of the reduction of the range of the parameter uncertainty that is predicted as a result of the parameter estimation using the future measurements. This implicit dual-control mechanism does not require a-priori tuning with respect to the relative importance of the probing actions against the optimal operation of the system, as proposed in other recent approaches. The results from a reactor control example show the advantage of using Dual Multi-stage NMPC over its robust adaptive counterpart, where the reduction of the uncertainty is not predicted and optimized, but only obtained a posteriori when the measurements have arrived.