Improving Scenario Decomposition for Multistage MPC using a Sensitivity-based Path-following Algorithm

Abstract

This letter proposes a computationally efficient algorithm for robust multistage scenario model predictive control (MPC). In multistage scenario MPC, the evolution of uncertainty in the prediction horizon is represented via a scenario tree. The resulting large-scale optimization problem can be decomposed into several smaller subproblems where, for example, each subproblem solves a single scenario. Since the different scenarios differ only in the uncertain parameters, the distributed scenario MPC problem can be cast as a parametric nonlinear programming (NLP) problem. By using the NLP sensitivity, we do not need to solve all the subproblems as full NLPs. Instead they can be solved exploiting the parametric nature by a path-following predictor-corrector algorithm that approximates the NLP. This results in a computationally efficient multistage scenario MPC framework. Simulation results show that the sensitivity-based distributed multistage MPC provides a very good approximation of the fully centralized scenario MPC.