A Framework for Embedded Model Predictive Control using Posits

Abstract

This paper proposes a framework for the high-accuracy, low-precision, and memory-efficient embedded model predictive control (MPC) using the posit™ numbers and its implementation on the ARM-based embedded platform. A quadratic programming (QP) problem in posit-based linear MPC is solved by the active set method (ASM) with a Cholesky factorization-based linear solver. The main idea of this paper is to encode all data associated with the QP problem as posit numbers and employ posit number arithmetic to synthesis the ASM algorithm. We provide a detailed analysis of a posit number that acts as a memory-efficient replacement of the IEEE 754 floating-point standard numbers. We show the posit-based ASM algorithm employed in MPC and its implementation on STM32 Nucleo-144 development board with STM32F746ZG MCU. The results of hardware-in-loop (HIL) simulations with the detailed analysis of memory utilization and performance of the posit-based ASM algorithm is shown with two case studies. HIL results show that the proposed approach can reduce memory footprints by 50% to 75% without losing control accuracy and performance.