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

more »

... the ADMM stepsize parameter for each scenario. We provide convergence analysis and derivethe 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. American Control Conference (ACC) This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Abstract-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.