Fast decentralized multi-stage model predictive control using sensitivity-based path-following and a nonsmooth Newton method

Abstract

This work addresses the challenge of computational complexity in Multistage Model Predictive Control (MPC). Multistage MPC is a robust control algorithm where uncertainty is accounted for by constructing a finite set of scenarios for different realizations of uncertainty. The resulting Multistage MPC problem becomes large and computationally expensive to solve. Several strategies have been proposed to reduce computation time and to make real-time implementation possible. A popular class of methods is decomposition methods, in which the Multistage MPC problem is decomposed into several smaller parametric subproblems that can be solved in parallel. The subproblems are repeatedly solved while a coordinator algorithm adjusts a parameter to recover the solution of the full problem. The main computational cost in this approach comes from (1) the coordinator algorithm requiring many iterations to converge, resulting in many resolves of the subproblems, and (2) the computational time to solve the subproblems. In this paper we propose a Predictor–Corrector based path-following algorithm to reduce the solution time of the subproblems for a primal-decomposition algorithm for Multistage MPC. A new Predictor–Corrector methodology based on nonsmooth equation solving is proposed with local superlinear/quadratic convergence. The algorithm path-follows along the parameter path given by the coordinator algorithm. Our path-following algorithm is combined with the Extended Newton algorithm from Bjorvand and Jäschke (2023) for reducing number of coordinator steps. The proposed algorithm is applied to a gas-lift system where the total number of iterations of the algorithm are significantly reduced compared to the standard primal decomposition algorithm for Multistage MPC.