Reducing the memory footprint of explicit MPC solutions by partial selection

Amount of memory needed to implement a given explicit model predictive control (MPC) feedback law is reduced without sacrificing performance. We show that a simpler equivalent explicit feedback can be obtained by selecting a particular subset of controller regions. Since the procedure requires almost no pre-processing, it is easily applicable to reduce complexity of explicit MPC solutions with arbitrary number of regions and/or with high state dimensions. Significant reduction of memory consumption is traded for on-line computation. In particular, evaluating the simpler feedback requires projecting a given point onto a non-convex set. A simple algorithm is provided to perform this task with favorable runtime complexity. Achievable reduction of the memory footprint is quantified and several motivating case studies are discussed.