A Memory-Efficient Explicit Model Predictive Control using Posits

For explicit model predictive control (EMPC), off-line pre-computed optimal feedback laws need to be stored in a look-up table for on-line evaluation. The need for memory to store the look-up table on embedded hardware limits applicability of EMPC to systems with few states, a small number of constraints, and short prediction horizons. In this paper, we present a novel technique to reduce the memory footprints of EMPC solutions. The idea is based on encoding all data (i.e., the critical regions and the feedback laws) as positTM numbers, which can be viewed as a memory-efficient replacement for the IEEE 754 floating-point standard. By using the posit number system, we achieve more accuracy with fewer bits, and posits can be efficiently deployed on embedded hardware like PLC, FPGA, DSP, ARM, etc. We show the design and implementation of posit-based EMPC for the control of the coupled tank system. Results show that the total memory footprints can be reduced by 75% without losing control accuracy. An additional advantage of the approach is that it can be applied on the top of existing complexity reduction techniques.