Analytical expression of explicit MPC solution via lattice piecewise-affine function

An analytical expression of the explicit solution to linear model predictive control (MPC) is proposed by the introduction of a lattice piecewise-affine (PWA) function. A systematic procedure is developed for building a lattice PWA representation from a continuous explicit MPC solution obtained by a multi-parametric program. A simple method is presented to remove the redundant parameters in the lattice expression of MPC control laws. The effectiveness of this approach is supported by the study of three benchmark MPC problems. The proposed analytical expression provides a very efficient and practically viable method for implementing the explicit MPC solutions regarding its online calculation and memory space requirements.