Decomposition via ADMM for scenario-based Model Predictive Control

We present a scenario-decomposition based Alternating Direction Method of Multipliers (ADMM) algorithm for the efficient solution of scenario-based Model Predictive Control (MPC) problems which arise for instance in the control of stochastic systems. We duplicate the variables involved in the non-anticipativity constraints which allows to develop an ADMM algorithm in which the computations scale linearly in the number of scenarios. Further, the decomposition allows for using different values of the ADMM stepsize parameter for each scenario. We provide convergence analysis and derive the optimal selection of the parameter for each scenario. The proposed approach outperforms the non-decomposed ADMM approach and compares favorably with Gurobi, a commercial QP solver, on a number of MPC problems derived from stopping control of a transportation system.