An efficient distributed algorithm for multi-stage robust nonlinear predictive control

This paper presents an algorithmic development in the framework of computationally efficient robust Nonlinear Model Predictive Control (NMPC) which deals with a parametric plant-model mismatch, where the description of the evolution of the uncertainty is done using a scenario tree, known as multi-stage approach. In order to reduce the computational time and memory requirements of the multistage NMPC, the calculations of the optimal control inputs can be done scenario-wise in parallel. These parallelized calculations must enforce the satisfaction of the non-anticipativity constraints, which is negotiated iteratively among the scenarios using Lagrangean or price-driven decomposition. The main challenge in using such scheme is the determination of the values of the aggregate variables that are used to coordinate the scenario-wise computations for convergence to the feasibility of the non-anticipativity constraints. The proposed approach uses parametric sensitivities of the optimal model states with respect to the control inputs which are used for the iterative determination of the values of aggregated variables. The proposed method achieves good performance and faster convergence compared to traditional decomposition schemes. The potential of the approach is demonstrated in simulation example of an hydrodesulphurisation unit.