A practical open-source approach to Model Predictive Control using the Legendre–Gauss–Radau pseudospectral method

In a world increasingly reliant on technologies that sense and respond to their environment – from thermostats to energy grids – predictive capabilities are critical. However, uncertainties and complexity often hinder the adoption of advanced strategies like Model Predictive Control (MPC), leading many industries to rely on simpler, less effective methods. This paper presents a practical, open-source software tool based on the Legendre–Gauss–Radau pseudospectral method, designed to streamline MPC implementation. The software handles dynamics, constraints, and objectives efficiently while supporting black-box systems. A case study in this paper demonstrates its effectiveness, with additional examples in the supplementary material validating its versatility.