Evaluation of piecewise affine control law via graph traversal

This paper presents a constructive algorithm for the effective evaluation of the piecewise affine (PWA) control laws generated in explicit model predictive control (MPC). One of the main limitations of explicit MPC is the construction of the search trees that are used to efficiently compute the PWA control law in real-time. The key idea developed in the paper consists in replacing these search trees by graphs that are directly generated while solving the multiparametric problems. It is shown that if the parameter space is explored in the breadth-first search (BFS) fashion, the bounds for the worst case runtime implementation can be obtained after the construction of an explicit solution. The proposed method traverses the graph in linear time that corresponds to a breadth of the graph on the average. Effectiveness of the approach is demonstrated numerically on a power electronics benchmark.