On Region-Free Explicit Model Predictive Control

Abstract We show that explicit MPC solutions admit a closed-form solution which does not require the storage of critical regions. Therefore significant amount of memory can be saved. In fact, not even the construction of such regions is required. Instead, all possible optimal active sets are first extensively enumerated. Then, for each optimal, only the analytical expressions of primal and dual variables are stored. Optimality of a particular if checked by verifying primal and dual feasibility conditions, which are unique for all candidate sets. We show that the required memory storage can be further reduced by only storing the factors for the dual variables. IEEE Conference on Decision and Control (CDC) 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 show that explicit MPC solutions admit a closed-form solution which does not require the storage of critical regions. Therefore significant amount of memory can be saved. In fact, not even the construction of such regions is required. Instead, all possible optimal active sets are first extensively enumerated. Then, for each optimal , only the analytical expressions of primal and dual variables are stored. Optimality of a particular if checked by verifying primal and dual feasibility conditions, which are unique for all candidate sets. We show that the required memory storage can be further reduced by only storing the factors for the dual variables