Approximate explicit model predictive control incorporating heuristics

Explicit piecewise linear state feedback solutions to the constrained linear model predictive control problem have recently been characterized and computed numerically using multiparametric quadratic programming. The piecewise linear state feedback is defined on a polyhedral partitioning of the state space, which may be quite complex. Here we suggest an approximate multi-parametric quadratic programming approach, which has the advantages that the partition is structured as a binary search tree. This leads to real-time computation of the piecewise linear state feedback with a computational complexity that is logarithmic with respect to the number of regions in the partition. The algorithm is based on heuristic rules that are used to partition the state space and estimate the approximation error.