Memory-Efficient Mixed-Precision Implementations for Robust Explicit Model Predictive Control

We propose an optimization for space-efficient implementations of explicit model-predictive controllers (MPC) for robust control of linear time-invariant (LTI) systems on embedded platforms. We obtain an explicit-form robust model-predictive controller as a solution to a multi-parametric linear programming problem. The structure of the controller is a polyhedral decomposition of the control domain, with an affine map for each domain. While explicit MPC is suited for embedded devices with low computational power, the memory requirements for such controllers can be high. We provide an optimization algorithm for a mixed-precision implementation of the controller, where the deviation of the implemented controller from the original one is within the robustness margin of the robust control problem. The core of the mixed-precision optimization is an iterative static analysis that co-designs a robust controller and a low-bitwidth approximation that is statically guaranteed to always be within the robustness margin of the original controller. We have implemented our algorithm and show on a set of benchmarks that our optimization can reduce space requirements by up to 20.9% and on average by 12.6% compared to a minimal uniform precision implementation of the original controller.