Explicit model predictive control accuracy analysis

TL;DR

This paper analyzes how quantization affects the accuracy of explicit Model Predictive Control (MPC) implementations on micro-controllers, providing bounds to ensure desired control precision.

Contribution

It derives upper bounds on control error due to quantization, linking accuracy to the number of bits used in data representation.

Findings

Derived bounds for control input error based on quantization bits

Provided guidelines for selecting quantization levels to guarantee accuracy

Enhanced understanding of trade-offs between cost, speed, and precision in explicit MPC

Abstract

Model Predictive Control (MPC) can efficiently control constrained systems in real-time applications. MPC feedback law for a linear system with linear inequality constraints can be explicitly computed off-line, which results in an off-line partition of the state space into non-overlapped convex regions, with affine control laws associated to each region of the partition. An actual implementation of this explicit MPC in low cost micro-controllers requires the data to be "quantized", i.e. represented with a small number of memory bits. An aggressive quantization decreases the number of bits and the controller manufacturing costs, and may increase the speed of the controller, but reduces accuracy of the control input computation. We derive upper bounds for the absolute error in the control depending on the number of quantization bits and system parameters. The bounds can be used to determine how many quantization bits are needed in order to guarantee a specific level of accuracy in the control input.