Robust Dual Multi-stage NMPC using Guaranteed Parameter Estimation

Abstract

In this paper we present an implicit dual robust nonlinear model predictive control (NMPC) in the framework of (bounded-error) guaranteed parameter estimation and multi-stage NMPC, which uses a scenario tree to represent propagation of parametric model uncertainty through a dynamic system. The proposed implicit dual control scheme excites the system if the excitation signals improve the overall performance of the controller. A box (over-)approximation of the solution set of guaranteed parameter estimation which encloses the true parameter values is obtained by solving an optimization problem. The proposed approach uses approximations of the future solution sets and updates the scenario tree of the multi-stage NMPC along the prediction horizon accordingly. This gives rise to a bi-level optimization problem, which is solved as a single-level problem by implicitly solving the lower-level problem using its KKT conditions. The advantages of the proposed approach over the standard multi-stage NMPC are demonstrated for a linear and nonlinear (semi-batch reactor) simulation case studies.