Explicit spline-based continuous-time MPC: a study on design and performance

Abstract

This paper presents a continuous-time model predictive control scheme based on B-spline functions used for signals and model approximation. The proposed controller offers two interesting advantages. First, it formulates the control signal as a continuous polynomial spline function, the nature of which is determined by its control polygon that is subject of optimization. Second, all continuous constraints assumed over prediction horizon are consistently transformed into constraints imposed on a finite number of elements of this control polygon. Using parametric quadratic programming we further show how to obtain an explicit representation of the proposed controller, which is known for its efficient online implementation. The featured simulation study demonstrates that by a suitable choice of number and position of knots of the spline function over the prediction horizon it is possible to substantially reduce the number of critical regions of the explicit controller while preserving control performance, and to mitigate the direct correlation between number of regions and chosen length of prediction horizon.