Florin Stoican
University Politehnica of Bucharest, Bucharest, Romania

Model Predictive Control (MPC) is a popular control strategy which has proved its mettle in both theoretical and industrial process control applications. Essentially, MPC is a feedback control problem that uses an accurate model of the process to predict the evolution of its state vector and optimize a sequence of constrained control actions over a finite time horizon. One of its variants is the explicit MPC formulation which exploits the multi-parametric nature of the optimization program This material provides new methods for the construction, storage and retrieval of the explicit MPC solution in the case with quadratic cost and linear constraints. By exploiting the geometric interpretation of the MPC problem, we:
i) construct the explicit solution (i.e., enumerate the critical regions and associated affine laws) in an efficient manner;
ii) store it as a partially ordered set; and iii) provide a modified graph traversal algorithm for efficient point location (i.e., identifying the currently active critical region and its associated control law).