Approximate explicit constrained linear model predictive control via orthogonal search tree

Solutions to constrained linear model predictive control problems can be pre-computed off-line in an explicit form as a piecewise linear state feedback on a polyhedral partition of the state space, avoiding real-time optimization. We suggest an algorithm that will determine an approximate explicit piecewise linear state feedback by imposing an orthogonal search tree structure on the partition. This leads to a real-time computational complexity that is logarithmic in the number of regions in the partition, and the algorithm yields guarantees on the sub-optimality, asymptotic stability and constraint fulfillment.